메뉴 건너뛰기




Volumn 2, Issue , 2002, Pages 885-982

Chapter 17 Global attractors in partial differential equations

(1)  Raugel, G a  

a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0038815248     PISSN: 1874575X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-575X(02)80038-8     Document Type: Chapter
Times cited : (164)

References (224)
  • 1
    • 0347640946 scopus 로고
    • Comportement asymptotique de certaines équations aux dérivées partielles dissipatives
    • Université de Paris-Sud, Orsay
    • Abounouh M. Comportement asymptotique de certaines équations aux dérivées partielles dissipatives. Thesis (1993), Université de Paris-Sud, Orsay
    • (1993) Thesis
    • Abounouh, M.1
  • 2
    • 38249001273 scopus 로고
    • Asymptotic behaviour for a weakly damped Schrödinger equation in dimension two
    • Abounouh M. Asymptotic behaviour for a weakly damped Schrödinger equation in dimension two. Appl. Math. Lett. 6 (1993) 29-32
    • (1993) Appl. Math. Lett. , vol.6 , pp. 29-32
    • Abounouh, M.1
  • 3
    • 0000329412 scopus 로고
    • The Morse-Smale property for a semilinear parabolic equation
    • Angenent S.B. The Morse-Smale property for a semilinear parabolic equation. J. Differential Equations 62 (1986) 427-442
    • (1986) J. Differential Equations , vol.62 , pp. 427-442
    • Angenent, S.B.1
  • 4
    • 33646918069 scopus 로고
    • The dynamics of rotating waves in scalar reaction diffusion equations
    • Angenent S.B., and Fiedler B. The dynamics of rotating waves in scalar reaction diffusion equations. Trans. Amer. Math. Soc. 307 (1988) 545-568
    • (1988) Trans. Amer. Math. Soc. , vol.307 , pp. 545-568
    • Angenent, S.B.1    Fiedler, B.2
  • 5
    • 0000998760 scopus 로고
    • A damped hyperbolic equation with critical exponent
    • Arrieta J., Carvalho A., and Hale J.K. A damped hyperbolic equation with critical exponent. Comm. PDE 17 (1992) 841-866
    • (1992) Comm. PDE , vol.17 , pp. 841-866
    • Arrieta, J.1    Carvalho, A.2    Hale, J.K.3
  • 7
    • 0347536728 scopus 로고
    • Continuous dependence of attractors on the shape of domain
    • Boundary Value Problems of Mathematical Physics and Adjacent Problems of Function Theory, Vol. 26 Work collection dedicated to N.N. Ural'tseva on her annivers. Ladyzhenskaya O.A. (Ed), Nauka, Sankt-Peterburg
    • Babin A.V., and Pilyugin S.Y. Continuous dependence of attractors on the shape of domain. In: Ladyzhenskaya O.A. (Ed). Boundary Value Problems of Mathematical Physics and Adjacent Problems of Function Theory, Vol. 26 Work collection dedicated to N.N. Ural'tseva on her annivers. Zap. Nauchn. Semin. POMI 221 (1995), Nauka, Sankt-Peterburg 58-66
    • (1995) Zap. Nauchn. Semin. POMI , vol.221 , pp. 58-66
    • Babin, A.V.1    Pilyugin, S.Y.2
  • 8
    • 0001753772 scopus 로고
    • Regular attractors of semigroups and evolution equations
    • Babin A.V., and Vishik M.I. Regular attractors of semigroups and evolution equations. J. Math. Pures Appl. 62 (1983) 441-491
    • (1983) J. Math. Pures Appl. , vol.62 , pp. 441-491
    • Babin, A.V.1    Vishik, M.I.2
  • 9
    • 67649309337 scopus 로고
    • On the stationary curves and unstable invariant manifolds in the neighbor-hood of critical points of evolution equations depending on a parameter
    • English; Russian original
    • English; Russian original. Babin A.V., and Vishik M.I. On the stationary curves and unstable invariant manifolds in the neighbor-hood of critical points of evolution equations depending on a parameter. Soviet Math. Dokl. 31 (1985) 10-14
    • (1985) Soviet Math. Dokl. , vol.31 , pp. 10-14
    • Babin, A.V.1    Vishik, M.I.2
  • 10
    • 25444461010 scopus 로고
    • Unstable invariant sets of semigroups of non-linear operators and their per-turbations
    • English; Russian original
    • English; Russian original. Babin A.V., and Vishik M.I. Unstable invariant sets of semigroups of non-linear operators and their per-turbations. Russian Math. Surveys 41 (1986) 1-41
    • (1986) Russian Math. Surveys , vol.41 , pp. 1-41
    • Babin, A.V.1    Vishik, M.I.2
  • 11
    • 67649355850 scopus 로고
    • Uniform asymptotic solutions of a singularly perturbed evolutionary equation
    • in Russian
    • in Russian. Babin A.V., and Vishik M.I. Uniform asymptotic solutions of a singularly perturbed evolutionary equation. Uspekhi Mat. Nauk 42 (1987) 231-232
    • (1987) Uspekhi Mat. Nauk , vol.42 , pp. 231-232
    • Babin, A.V.1    Vishik, M.I.2
  • 12
    • 33747169742 scopus 로고
    • Uniform finite-parameter asymptotics of solutions of nonlinear evolutionary equations
    • Babin A.V., and Vishik M.I. Uniform finite-parameter asymptotics of solutions of nonlinear evolutionary equations. J. Math. Pures Appl. 68 (1989) 399-455
    • (1989) J. Math. Pures Appl. , vol.68 , pp. 399-455
    • Babin, A.V.1    Vishik, M.I.2
  • 14
    • 84894282888 scopus 로고
    • Attractors of damped wave equations
    • Germany
    • Ball J.M. Attractors of damped wave equations. Conference at Oberwolfach. Germany (1992)
    • (1992) Conference at Oberwolfach
    • Ball, J.M.1
  • 15
    • 0000938708 scopus 로고    scopus 로고
    • Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations
    • Ball J.M. Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations. J. Nonlinear Sci. 7 (1997) 475-502
    • (1997) J. Nonlinear Sci. , vol.7 , pp. 475-502
    • Ball, J.M.1
  • 16
    • 33645761741 scopus 로고    scopus 로고
    • Erratum: "Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations"
    • Ball J.M. Erratum: "Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations". J. Nonlinear Sci. 8 (1998) 233
    • (1998) J. Nonlinear Sci. , vol.8 , pp. 233
    • Ball, J.M.1
  • 17
    • 0026923885 scopus 로고
    • Sharp sufficient conditions for the observation, control, and stabiliza-tion of waves from the boundary
    • Bardos C., Lebeau G., and Rauch J. Sharp sufficient conditions for the observation, control, and stabiliza-tion of waves from the boundary. SIAM J. Control Optimization 30 (1992) 1024-1065
    • (1992) SIAM J. Control Optimization , vol.30 , pp. 1024-1065
    • Bardos, C.1    Lebeau, G.2    Rauch, J.3
  • 18
    • 33748532060 scopus 로고    scopus 로고
    • Navier-Stokes equations and dynamical systems
    • Fiedler B. (Ed), Elsevier, Amsterdam
    • Bardos C., and Nicolaenko B. Navier-Stokes equations and dynamical systems. In: Fiedler B. (Ed). Handbook for Dynamical Systems Vol. 2 (2002), Elsevier, Amsterdam 503-597
    • (2002) Handbook for Dynamical Systems , vol.2 , pp. 503-597
    • Bardos, C.1    Nicolaenko, B.2
  • 19
    • 0015768944 scopus 로고
    • Sur l'unicité rétrograde des équations paraboliques et quelques équations voi-sines
    • Bardos C., and Tartar L. Sur l'unicité rétrograde des équations paraboliques et quelques équations voi-sines. Arch. Rational Mech. Anal. 50 (1973) 10-25
    • (1973) Arch. Rational Mech. Anal. , vol.50 , pp. 10-25
    • Bardos, C.1    Tartar, L.2
  • 20
    • 0038351240 scopus 로고
    • Local Semi-Dynamical Systems
    • Springer, Berlin
    • Bhatia N.P., and Hajek O. Local Semi-Dynamical Systems. Lecture Notes in Math. Vol. 90 (1969), Springer, Berlin
    • (1969) Lecture Notes in Math. , vol.90
    • Bhatia, N.P.1    Hajek, O.2
  • 22
    • 0007160812 scopus 로고
    • The attractor of the scalar reaction-diffusion equation is a smooth graph
    • Brunovský P. The attractor of the scalar reaction-diffusion equation is a smooth graph. J. Dynamics Differential Equations 2 (1990) 293-323
    • (1990) J. Dynamics Differential Equations , vol.2 , pp. 293-323
    • Brunovský, P.1
  • 23
    • 0040174393 scopus 로고
    • Generic properties of stationary state solutions of reaction-diffusion equa-tions
    • Brunovský P., and Chow S.-N. Generic properties of stationary state solutions of reaction-diffusion equa-tions. J. Differential Equations 53 (1984) 1-23
    • (1984) J. Differential Equations , vol.53 , pp. 1-23
    • Brunovský, P.1    Chow, S.-N.2
  • 24
    • 0001168397 scopus 로고
    • Connecting orbits in scalar reaction diffusion equations. II: The complete solution
    • Brunovský P., and Fiedler B. Connecting orbits in scalar reaction diffusion equations. II: The complete solution. J. Differential Equations 81 (1989) 106-135
    • (1989) J. Differential Equations , vol.81 , pp. 106-135
    • Brunovský, P.1    Fiedler, B.2
  • 25
    • 0001645279 scopus 로고    scopus 로고
    • The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension
    • Brunovský P., and Poláčik P. The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. J. Differential Equations 135 (1997) 129-181
    • (1997) J. Differential Equations , vol.135 , pp. 129-181
    • Brunovský, P.1    Poláčik, P.2
  • 26
    • 0039460110 scopus 로고    scopus 로고
    • On the local structure of ω-limit sets of maps
    • Brunovský P., and Poláčik P. On the local structure of ω-limit sets of maps. Z. Angew. Math. Phys. 48 (1997) 976-986
    • (1997) Z. Angew. Math. Phys. , vol.48 , pp. 976-986
    • Brunovský, P.1    Poláčik, P.2
  • 28
    • 5244300569 scopus 로고
    • Introduction aux Problemes d'Evolution Semi-linéaires
    • Ellipses
    • Cazenave Th., and Haraux A. Introduction aux Problemes d'Evolution Semi-linéaires. Mathématiques et Applications Vol. 1 (1990), Ellipses
    • (1990) Mathématiques et Applications , vol.1
    • Cazenave, Th.1    Haraux, A.2
  • 29
    • 34248188202 scopus 로고
    • α-contractions and attractors for dissipative semilinear hyperbolic equations and systems
    • Ceron S., and Lopes O. α-contractions and attractors for dissipative semilinear hyperbolic equations and systems. Ann. Mat. Pura Appl. IV. Ser. 160 (1991) 193-206
    • (1991) Ann. Mat. Pura Appl. IV. Ser. , vol.160 , pp. 193-206
    • Ceron, S.1    Lopes, O.2
  • 30
    • 0016345113 scopus 로고
    • A bifurcation problem for a nonlinear parabolic equation
    • Chafee N., and Infante E.F. A bifurcation problem for a nonlinear parabolic equation. Appl. Anal. 4 (1974) 17-37
    • (1974) Appl. Anal. , vol.4 , pp. 17-37
    • Chafee, N.1    Infante, E.F.2
  • 31
    • 0000645209 scopus 로고
    • Structural stability for time periodic one dimensional parabolic equations
    • Chen M., Chen X.-Y., and Hale J.K. Structural stability for time periodic one dimensional parabolic equations. J. Differential Equations 96 (1992) 355-418
    • (1992) J. Differential Equations , vol.96 , pp. 355-418
    • Chen, M.1    Chen, X.-Y.2    Hale, J.K.3
  • 32
    • 0032328374 scopus 로고    scopus 로고
    • A strong unique continuation theorem for parabolic equations
    • Chen X.-Y. A strong unique continuation theorem for parabolic equations. Math. Ann. 311 (1998) 603-630
    • (1998) Math. Ann. , vol.311 , pp. 603-630
    • Chen, X.-Y.1
  • 34
    • 0001530660 scopus 로고
    • Attractors of nonautonomous dynamical systems and their dimension
    • Chepyzhov V.V., and Vishik M.I. Attractors of nonautonomous dynamical systems and their dimension. J. Math. Pures Appl. 73 (1994) 279-333
    • (1994) J. Math. Pures Appl. , vol.73 , pp. 279-333
    • Chepyzhov, V.V.1    Vishik, M.I.2
  • 36
    • 0347576335 scopus 로고
    • A note of continuity of semigroups of maps
    • Chernoff P. A note of continuity of semigroups of maps. Proc. Amer. Math. Soc. 53 (1975) 318-320
    • (1975) Proc. Amer. Math. Soc. , vol.53 , pp. 318-320
    • Chernoff, P.1
  • 37
    • 84966220944 scopus 로고
    • On continuity and smoothness of group actions
    • Chernoff P., and Marsden J. On continuity and smoothness of group actions. Bull. Amer. Math. Soc. 76 (1970) 104-1049
    • (1970) Bull. Amer. Math. Soc. , vol.76 , pp. 104-1049
    • Chernoff, P.1    Marsden, J.2
  • 39
    • 38249029133 scopus 로고
    • Invariant manifolds for flows in Banach spaces
    • Chow S.-N., and Lu K. Invariant manifolds for flows in Banach spaces. J. Differential Equations 74 (1988) 285-317
    • (1988) J. Differential Equations , vol.74 , pp. 285-317
    • Chow, S.-N.1    Lu, K.2
  • 40
    • 0039530497 scopus 로고    scopus 로고
    • Theory of functional that uniquely determine the asymptotic dynamics of infinite-dimensional dissipative systems
    • Chueshov I. Theory of functional that uniquely determine the asymptotic dynamics of infinite-dimensional dissipative systems. Russian Math. Surveys 53 (1998) 731-776
    • (1998) Russian Math. Surveys , vol.53 , pp. 731-776
    • Chueshov, I.1
  • 41
    • 0002836308 scopus 로고    scopus 로고
    • Uspekhi Mat. Nauk 53 (1998) 77-124
    • (1998) Uspekhi Mat. Nauk , vol.53 , pp. 77-124
  • 42
    • 0039459032 scopus 로고    scopus 로고
    • Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems
    • Cockburn B., Jones D., and Titi E. Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems. Math. Comput. 66 (1997) 1073-1087
    • (1997) Math. Comput. , vol.66 , pp. 1073-1087
    • Cockburn, B.1    Jones, D.2    Titi, E.3
  • 44
    • 21144482383 scopus 로고
    • A global attracting set for the Kuramoto-Sivashinsky equation
    • Collet P., Eckmann J.-R., Epstein H., and Stubbe J. A global attracting set for the Kuramoto-Sivashinsky equation. Comm. Math. Phys. 152 (1993) 203-214
    • (1993) Comm. Math. Phys. , vol.152 , pp. 203-214
    • Collet, P.1    Eckmann, J.-R.2    Epstein, H.3    Stubbe, J.4
  • 45
    • 84990581938 scopus 로고
    • Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations
    • Constantin P., and Foias C. Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations. Comm. Pure Appl. Math. 38 (1985) 1-27
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 1-27
    • Constantin, P.1    Foias, C.2
  • 47
  • 48
    • 0346128616 scopus 로고
    • α-condensing maps and dissipative systems
    • Brown University, Providence, RI
    • Cooperman G. α-condensing maps and dissipative systems. Ph.D. thesis (1978), Brown University, Providence, RI
    • (1978) Ph.D. thesis
    • Cooperman, G.1
  • 50
    • 0001050862 scopus 로고
    • Semiflows generated by compact and uniform processes
    • Dafermos C. Semiflows generated by compact and uniform processes. Math. Systems Theory 8 (1975) 142-149
    • (1975) Math. Systems Theory , vol.8 , pp. 142-149
    • Dafermos, C.1
  • 51
    • 0002541268 scopus 로고
    • Asymptotic behavior of solutions of evolution equations
    • Madison, WI, 1977
    • Dafermos C. Asymptotic behavior of solutions of evolution equations. Nonlinear Evolution Equations, Proc. Symp. Madison, WI, 1977 (1978) 103-123
    • (1978) Nonlinear Evolution Equations, Proc. Symp. , pp. 103-123
    • Dafermos, C.1
  • 52
    • 0032325270 scopus 로고    scopus 로고
    • Hausdorff Dimension of a random invariant set
    • Debussche A. Hausdorff Dimension of a random invariant set. J. Math. Pures Appl. 77 (1998) 967-988
    • (1998) J. Math. Pures Appl. , vol.77 , pp. 967-988
    • Debussche, A.1
  • 54
    • 0011505857 scopus 로고
    • Semi-groups of maps in a locally compact space
    • Dorroh J. Semi-groups of maps in a locally compact space. Canad. J. Math. 19 (1967) 688-696
    • (1967) Canad. J. Math. , vol.19 , pp. 688-696
    • Dorroh, J.1
  • 55
    • 0000260838 scopus 로고
    • Dimension de Hausdorff des attracteurs
    • Douady A., and Oesterlé J. Dimension de Hausdorff des attracteurs. C. R. Acad. Sci. Paris 290 (1980) 1135-1138
    • (1980) C. R. Acad. Sci. Paris , vol.290 , pp. 1135-1138
    • Douady, A.1    Oesterlé, J.2
  • 57
    • 0003240970 scopus 로고
    • Exponential Attractors for Dissipative Evolution Equations
    • Masson, Paris
    • Eden A., Foias C., Nicolaenko B., and Temam R. Exponential Attractors for Dissipative Evolution Equations. RAM Vol. 37 (1994), Masson, Paris
    • (1994) RAM , vol.37
    • Eden, A.1    Foias, C.2    Nicolaenko, B.3    Temam, R.4
  • 58
    • 0001082769 scopus 로고
    • Attractors in inhomogeneous conservation laws and parabolic regularizations
    • Fan H., and Hale J.K. Attractors in inhomogeneous conservation laws and parabolic regularizations. Trans. Amer. Math. Soc. 347 (1995) 1239-1254
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 1239-1254
    • Fan, H.1    Hale, J.K.2
  • 60
    • 84973937932 scopus 로고
    • Asymptotic behaviour and attractors for a semilinear damped wave equation with supercritical exponent
    • Feireisl E. Asymptotic behaviour and attractors for a semilinear damped wave equation with supercritical exponent. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 1051-1062
    • (1995) Proc. Roy. Soc. Edinburgh Sect. A , vol.125 , pp. 1051-1062
    • Feireisl, E.1
  • 62
    • 84947513673 scopus 로고
    • Global attractors for semilinear wave equations with locally distributed non-linear damping and critical exponent
    • Feireisl E., and Zuazua E. Global attractors for semilinear wave equations with locally distributed non-linear damping and critical exponent. Comm. Partial Differential Equations 18 (1993) 1539-1555
    • (1993) Comm. Partial Differential Equations , vol.18 , pp. 1539-1555
    • Feireisl, E.1    Zuazua, E.2
  • 63
    • 0002062139 scopus 로고    scopus 로고
    • Gevrey regularity for nonlinear analytic parabolic equations
    • Ferrari A., and Titi E. Gevrey regularity for nonlinear analytic parabolic equations. Comm. Partial Differ-ential Equations 23 (1998) 1-16
    • (1998) Comm. Partial Differ-ential Equations , vol.23 , pp. 1-16
    • Ferrari, A.1    Titi, E.2
  • 64
    • 0001794246 scopus 로고
    • Global attractors of one-dimensional parabolic equations: Sixteen examples
    • Fiedler B. Global attractors of one-dimensional parabolic equations: Sixteen examples. Tatra Mt. Math. Publ. 4 (1994) 67-92
    • (1994) Tatra Mt. Math. Publ. , vol.4 , pp. 67-92
    • Fiedler, B.1
  • 65
    • 0002646555 scopus 로고    scopus 로고
    • Do global attractors depend on boundary conditions?
    • Fiedler B. Do global attractors depend on boundary conditions?. Doc. Math. J. DMV 1 (1996) 215-228
    • (1996) Doc. Math. J. DMV , vol.1 , pp. 215-228
    • Fiedler, B.1
  • 66
    • 0000980087 scopus 로고
    • A Poincaré-Bendixson theorem for scalar reaction diffusion equations
    • Fiedler B., and Mallet-Paret J. A Poincaré-Bendixson theorem for scalar reaction diffusion equations. Arch. Rational Mech. Anal. 107 (1989) 325-345
    • (1989) Arch. Rational Mech. Anal. , vol.107 , pp. 325-345
    • Fiedler, B.1    Mallet-Paret, J.2
  • 67
    • 84974103874 scopus 로고
    • Complicated dynamics of scalar reaction diffusion equations with a nonlocal term
    • Fiedler B., and Poláčik P. Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990) 167-192
    • (1990) Proc. Roy. Soc. Edinburgh Sect. A , vol.115 , pp. 167-192
    • Fiedler, B.1    Poláčik, P.2
  • 68
    • 0030577735 scopus 로고    scopus 로고
    • Heteroclinic orbits of semilinear parabolic equations
    • Fiedler B., and Rocha C. Heteroclinic orbits of semilinear parabolic equations. J. Differential Equations 125 (1996) 239-281
    • (1996) J. Differential Equations , vol.125 , pp. 239-281
    • Fiedler, B.1    Rocha, C.2
  • 69
    • 22844455201 scopus 로고    scopus 로고
    • Orbit equivalence of global attractors of semilinear parabolic differential equations
    • Fiedler B., and Rocha C. Orbit equivalence of global attractors of semilinear parabolic differential equations. Trans. Amer. Math. Soc. 352 (2000) 257-284
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 257-284
    • Fiedler, B.1    Rocha, C.2
  • 70
    • 0000202793 scopus 로고
    • Strongly damped quasilinear evolution equations
    • Fitzgibbon W. Strongly damped quasilinear evolution equations. J. Math. Anal. Appl. 79 (1981) 536-550
    • (1981) J. Math. Anal. Appl. , vol.79 , pp. 536-550
    • Fitzgibbon, W.1
  • 71
    • 0020830393 scopus 로고
    • Asymptotic analysis of the Navier-Stokes equations
    • Foias C., Manley O., Temam R., and Trêve Y. Asymptotic analysis of the Navier-Stokes equations. Phys. D 9 (1983) 157-188
    • (1983) Phys. D , vol.9 , pp. 157-188
    • Foias, C.1    Manley, O.2    Temam, R.3    Trêve, Y.4
  • 72
    • 0003169927 scopus 로고    scopus 로고
    • Finite fractal dimension and Hölder-Lipschitz parametrization
    • Foias C., and Olson E.J. Finite fractal dimension and Hölder-Lipschitz parametrization. Indiana Univ. Math. J. 45 (1996) 603-616
    • (1996) Indiana Univ. Math. J. , vol.45 , pp. 603-616
    • Foias, C.1    Olson, E.J.2
  • 73
    • 0002449201 scopus 로고
    • Sur le comportement global des solutions non stationnaires des équations de Navier-Stokes en dimension deux
    • Foias C., and Prodi G. Sur le comportement global des solutions non stationnaires des équations de Navier-Stokes en dimension deux. Rend. Sem. Mat. Univ. Padova 39 (1967) 1-34
    • (1967) Rend. Sem. Mat. Univ. Padova , vol.39 , pp. 1-34
    • Foias, C.1    Prodi, G.2
  • 74
    • 0000640733 scopus 로고
    • Inertial manifolds for nonlinear evolutionary equations
    • Foias C., Sell G., and Temam R. Inertial manifolds for nonlinear evolutionary equations. J. Differential Equations 73 (1988) 309-353
    • (1988) J. Differential Equations , vol.73 , pp. 309-353
    • Foias, C.1    Sell, G.2    Temam, R.3
  • 75
    • 0000263117 scopus 로고
    • Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
    • Foias C., and Temam R. Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations. J. Math. Pures Appl. 9 (1979) 339-368
    • (1979) J. Math. Pures Appl. , vol.9 , pp. 339-368
    • Foias, C.1    Temam, R.2
  • 76
    • 33746636159 scopus 로고
    • Gevrey class regularity for the solutions of the Navier-Stokes equations
    • Foias C., and Temam R. Gevrey class regularity for the solutions of the Navier-Stokes equations. J. Funct. Anal. 87 (1989) 359-369
    • (1989) J. Funct. Anal. , vol.87 , pp. 359-369
    • Foias, C.1    Temam, R.2
  • 77
    • 0002238002 scopus 로고
    • A permutation related to the dynamics of a scalar parabolic PDE
    • Fusco G., and Rocha C. A permutation related to the dynamics of a scalar parabolic PDE. J. Differential Equations 91 (1991) 111-137
    • (1991) J. Differential Equations , vol.91 , pp. 111-137
    • Fusco, G.1    Rocha, C.2
  • 78
    • 25744440201 scopus 로고    scopus 로고
    • in preparation, Cours de troisième cycle de l'Université d'Orsay
    • in preparation. Gallay Th., and Raugel G. Stabilité locale et globale (2000), Cours de troisième cycle de l'Université d'Orsay
    • (2000) Stabilité locale et globale
    • Gallay, Th.1    Raugel, G.2
  • 79
    • 33749333826 scopus 로고
    • Structure of the set of solutions of dissipative equations
    • Gerstein V.M., and Krasnosel'skij M.A. Structure of the set of solutions of dissipative equations. Dokl. Akad. Nauk SSSR 183 (1968) 267-269
    • (1968) Dokl. Akad. Nauk SSSR , vol.183 , pp. 267-269
    • Gerstein, V.M.1    Krasnosel'skij, M.A.2
  • 80
    • 0342670035 scopus 로고
    • Some backward uniqueness results
    • Ghidaglia J.-M. Some backward uniqueness results. Nonlinear Anal. TMA 10 (1986) 777-790
    • (1986) Nonlinear Anal. TMA , vol.10 , pp. 777-790
    • Ghidaglia, J.-M.1
  • 81
    • 0000864904 scopus 로고
    • Finite dimensional behavior for weakly damped driven Schrödinger equations
    • Ghidaglia J.-M. Finite dimensional behavior for weakly damped driven Schrödinger equations. Ann. Inst. H. Poincaré, Anal. Non Linéaire 5 (1988) 365-405
    • (1988) Ann. Inst. H. Poincaré, Anal. Non Linéaire , vol.5 , pp. 365-405
    • Ghidaglia, J.-M.1
  • 82
    • 0000616385 scopus 로고
    • Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dy-namical system in the long time
    • Ghidaglia J.-M. Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dy-namical system in the long time. J. Differential Equations 74 (1988) 369-390
    • (1988) J. Differential Equations , vol.74 , pp. 369-390
    • Ghidaglia, J.-M.1
  • 83
    • 0001005263 scopus 로고
    • A note on the strong convergence towards attractors of damped forced KdV equations
    • Ghidaglia J.-M. A note on the strong convergence towards attractors of damped forced KdV equations. J. Differential Equations 110 (1994) 356-359
    • (1994) J. Differential Equations , vol.110 , pp. 356-359
    • Ghidaglia, J.-M.1
  • 84
    • 0000322045 scopus 로고
    • Dimension of the attractors associated to the Ginzburg-Landau partial differential equation
    • Ghidaglia J.-M., and Héron B. Dimension of the attractors associated to the Ginzburg-Landau partial differential equation. Phys. D 28 (1987) 282-304
    • (1987) Phys. D , vol.28 , pp. 282-304
    • Ghidaglia, J.-M.1    Héron, B.2
  • 85
    • 0001273746 scopus 로고
    • Regularity of the solutions of second order evolution equations and their attractors
    • Ghidaglia J.-M., and Temam R. Regularity of the solutions of second order evolution equations and their attractors. Ann. Sc. Norm. Super. Pisa Cl. Sci., IV 14 (1987) 485-511
    • (1987) Ann. Sc. Norm. Super. Pisa Cl. Sci., IV , vol.14 , pp. 485-511
    • Ghidaglia, J.-M.1    Temam, R.2
  • 86
    • 0000160580 scopus 로고
    • Attractors for damped nonlinear hyperbolic equations
    • Ghidaglia J.-M., and Temam R. Attractors for damped nonlinear hyperbolic equations. J. Math. Pures Appl. 9 (1987) 273-319
    • (1987) J. Math. Pures Appl. , vol.9 , pp. 273-319
    • Ghidaglia, J.-M.1    Temam, R.2
  • 87
    • 0030637309 scopus 로고    scopus 로고
    • On the connectedness of attractors for dynamical systems
    • Gobbino M., and Sardella M. On the connectedness of attractors for dynamical systems. J. Differential Equations 133 (1997) 1-14
    • (1997) J. Differential Equations , vol.133 , pp. 1-14
    • Gobbino, M.1    Sardella, M.2
  • 88
    • 85064027304 scopus 로고    scopus 로고
    • Regularity of the attractor for a weakly damped nonlinear Schrödinger equation
    • Goubet O. Regularity of the attractor for a weakly damped nonlinear Schrödinger equation. Appl. Anal. 60 (1996) 99-119
    • (1996) Appl. Anal. , vol.60 , pp. 99-119
    • Goubet, O.1
  • 91
    • 0034419781 scopus 로고    scopus 로고
    • Asymptotic smoothing effect for weakly damped forced Korteweg-de-Vries equations
    • Goubet O. Asymptotic smoothing effect for weakly damped forced Korteweg-de-Vries equations. Discrete and Continuous Dynamical Systems 6 (2000) 625-644
    • (2000) Discrete and Continuous Dynamical Systems , vol.6 , pp. 625-644
    • Goubet, O.1
  • 93
    • 0014492316 scopus 로고
    • Dynamical systems and stability
    • Hale J.K. Dynamical systems and stability. J. Math. Anal. Appl. 26 (1969) 39-59
    • (1969) J. Math. Anal. Appl. , vol.26 , pp. 39-59
    • Hale, J.K.1
  • 94
    • 0002627286 scopus 로고
    • Asymptotic behaviour and dynamics in infinite dimensions
    • Pitman, Boston
    • Hale J.K. Asymptotic behaviour and dynamics in infinite dimensions. Research Notes in Mathematics Vol. 132 (1985), Pitman, Boston 1-41
    • (1985) Research Notes in Mathematics , vol.132 , pp. 1-41
    • Hale, J.K.1
  • 95
    • 0003293929 scopus 로고
    • Asymptotic Behavior of Dissipative Systems
    • Amer. Math. Soc, Providence, RI
    • Hale J.K. Asymptotic Behavior of Dissipative Systems. Mathematical Surveys and Monographs Vol. 25 (1988), Amer. Math. Soc, Providence, RI
    • (1988) Mathematical Surveys and Monographs , vol.25
    • Hale, J.K.1
  • 96
    • 67649330340 scopus 로고
    • Attractors and Dynamics in PDE
    • Hale J.K. Attractors and Dynamics in PDE. NATO Lectures (1995)
    • (1995) NATO Lectures
    • Hale, J.K.1
  • 97
    • 0011726534 scopus 로고    scopus 로고
    • Dynamics of a scalar parabolic equation
    • Hale J.K. Dynamics of a scalar parabolic equation. Canad. Appl. Math. Quarterly 5 (1997) 209-305
    • (1997) Canad. Appl. Math. Quarterly , vol.5 , pp. 209-305
    • Hale, J.K.1
  • 98
    • 1042285852 scopus 로고    scopus 로고
    • Dynamics of numerical approximations
    • Hale J.K. Dynamics of numerical approximations. Appl. Math. Comput. 89 (1998) 5-15
    • (1998) Appl. Math. Comput. , vol.89 , pp. 5-15
    • Hale, J.K.1
  • 99
    • 33144478848 scopus 로고    scopus 로고
    • Dissipation and attractors
    • Berlin. International Conference on Differential Equations. Fiedler B. (Ed), World Scientific, Singapore
    • Berlin. Hale J.K. Dissipation and attractors. In: Fiedler B. (Ed). International Conference on Differential Equations. Proceedings of the Conference, Equadiff. 99 Vol. 1 (2000), World Scientific, Singapore 622-637
    • (2000) Proceedings of the Conference, Equadiff. 99 , vol.1 , pp. 622-637
    • Hale, J.K.1
  • 100
    • 67649328062 scopus 로고    scopus 로고
    • Unpublished notes
    • J.K. Hale, Unpublished notes.
    • Hale, J.K.1
  • 101
    • 0007082735 scopus 로고
    • Theory of a general class of dissipative processes
    • Hale J.K., LaSalle J.P., and Slemrod M. Theory of a general class of dissipative processes. J. Math. Anal. Appl. 39 (1972) 177-191
    • (1972) J. Math. Anal. Appl. , vol.39 , pp. 177-191
    • Hale, J.K.1    LaSalle, J.P.2    Slemrod, M.3
  • 102
    • 84948497651 scopus 로고
    • Upper semicontinuity of attractors for approximations of semigroups and partial differential equations
    • Hale J.K., Lin X.B., and Raugel G. Upper semicontinuity of attractors for approximations of semigroups and partial differential equations. Math. Comp. 50 (1988) 89-123
    • (1988) Math. Comp. , vol.50 , pp. 89-123
    • Hale, J.K.1    Lin, X.B.2    Raugel, G.3
  • 103
    • 0000266374 scopus 로고
    • Fixed point theorems and dissipative processes
    • Hale J.K., and Lopes O. Fixed point theorems and dissipative processes. J. Differential Equations 13 (1973) 391-402
    • (1973) J. Differential Equations , vol.13 , pp. 391-402
    • Hale, J.K.1    Lopes, O.2
  • 104
    • 0003898370 scopus 로고
    • An Introduction to Infinite Dimensional Dynamical Systems
    • Springer, Berlin
    • Hale J.K., Magalháes L., and Oliva W. An Introduction to Infinite Dimensional Dynamical Systems. Appl. Math. Sci. Vol. 47 (1984), Springer, Berlin
    • (1984) Appl. Math. Sci. , vol.47
    • Hale, J.K.1    Magalháes, L.2    Oliva, W.3
  • 105
    • 0000610074 scopus 로고
    • Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation
    • Hale J.K., and Raugel G. Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation. J. Differential Equations 73 (1988) 197-214
    • (1988) J. Differential Equations , vol.73 , pp. 197-214
    • Hale, J.K.1    Raugel, G.2
  • 106
    • 0012234921 scopus 로고
    • Lower semicontinuity of attractors of gradient systems and applications
    • Hale J.K., and Raugel G. Lower semicontinuity of attractors of gradient systems and applications. Ann. Mat. Pura Appl. (IV) CLIV (1989) 281-326
    • (1989) Ann. Mat. Pura Appl. (IV) , vol.CLIV , pp. 281-326
    • Hale, J.K.1    Raugel, G.2
  • 107
    • 0002931112 scopus 로고
    • Lower Semicontinuity of the attractor for a singularly perturbed hyperbolic equation
    • Hale J.K., and Raugel G. Lower Semicontinuity of the attractor for a singularly perturbed hyperbolic equation. J. Dynamics Differential Equations 2 (1990) 19-67
    • (1990) J. Dynamics Differential Equations , vol.2 , pp. 19-67
    • Hale, J.K.1    Raugel, G.2
  • 108
    • 0001512085 scopus 로고
    • A damped hyperbolic equation on thin domains
    • Hale J.K., and Raugel G. A damped hyperbolic equation on thin domains. Trans. Amer. Math. Soc. 329 (1992) 185-219
    • (1992) Trans. Amer. Math. Soc. , vol.329 , pp. 185-219
    • Hale, J.K.1    Raugel, G.2
  • 109
    • 0002555899 scopus 로고
    • Convergence in gradient-like systems
    • Hale J.K., and Raugel G. Convergence in gradient-like systems. ZAMP 43 (1992) 63-124
    • (1992) ZAMP , vol.43 , pp. 63-124
    • Hale, J.K.1    Raugel, G.2
  • 110
    • 0002081870 scopus 로고
    • Reaction-diffusion equation on thin domains
    • Hale J.K., and Raugel G. Reaction-diffusion equation on thin domains. J. Math. Pures Appl. 71 (1992) 33-95
    • (1992) J. Math. Pures Appl. , vol.71 , pp. 33-95
    • Hale, J.K.1    Raugel, G.2
  • 111
    • 0003065470 scopus 로고
    • Attractors for dissipative evolutionary equations
    • 2 (Barcelona 1991), World Scientific, River Edge, NJ
    • 2 (Barcelona 1991). Hale J.K., and Raugel G. Attractors for dissipative evolutionary equations. International Conference on Differential Equations Vols. 1 (1993), World Scientific, River Edge, NJ 3-22
    • (1993) International Conference on Differential Equations , vol.1 , pp. 3-22
    • Hale, J.K.1    Raugel, G.2
  • 112
    • 0011020485 scopus 로고
    • Limits of semigroups depending on parameters
    • Hale J.K., and Raugel G. Limits of semigroups depending on parameters. Resenhas 1 (1993) 1-45
    • (1993) Resenhas , vol.1 , pp. 1-45
    • Hale, J.K.1    Raugel, G.2
  • 113
    • 84971123031 scopus 로고
    • A reaction-diffusion equation on a thin L-shaped domain
    • Hale J.K., and Raugel G. A reaction-diffusion equation on a thin L-shaped domain. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 283-327
    • (1995) Proc. Roy. Soc. Edinburgh Sect. A , vol.125 , pp. 283-327
    • Hale, J.K.1    Raugel, G.2
  • 116
    • 0040258664 scopus 로고
    • Smoothness of bounded solutions of nonlinear evolution equations
    • Hale J.K., and Scheurle J. Smoothness of bounded solutions of nonlinear evolution equations. J. Differen-tial Equations 56 (1985) 142-163
    • (1985) J. Differen-tial Equations , vol.56 , pp. 142-163
    • Hale, J.K.1    Scheurle, J.2
  • 117
    • 0003324723 scopus 로고
    • Introduction to Functional Differential Equations
    • Springer, Berlin
    • Hale J.K., and Verduyn-Lunel S. Introduction to Functional Differential Equations. Appl. Math. Sci. Vol. 99 (1993), Springer, Berlin
    • (1993) Appl. Math. Sci. , vol.99
    • Hale, J.K.1    Verduyn-Lunel, S.2
  • 118
    • 0002028112 scopus 로고
    • Two Remarks on dissipative hyperbolic problems
    • Vol. 7. Séminaire du Collège de France, Pitman
    • Vol. 7. Haraux A. Two Remarks on dissipative hyperbolic problems. Séminaire du Collège de France. Res. Notes Math. Vol. 122 (1985), Pitman 161-179
    • (1985) Res. Notes Math. , vol.122 , pp. 161-179
    • Haraux, A.1
  • 119
    • 0003352405 scopus 로고
    • Systèmes Dynamiques Dissipatifs et Applications
    • Masson, Paris
    • Haraux A. Systèmes Dynamiques Dissipatifs et Applications. RMA Vol. 17 (1991), Masson, Paris
    • (1991) RMA , vol.17
    • Haraux, A.1
  • 121
    • 0002796050 scopus 로고    scopus 로고
    • Convergence of bounded weak solutions of the wave equation with dissi-pation and analytic nonlinearity
    • Haraux A., and Jendoubi M.A. Convergence of bounded weak solutions of the wave equation with dissi-pation and analytic nonlinearity. Calc. Var. Partial Differential Equations 9 (1999) 95-124
    • (1999) Calc. Var. Partial Differential Equations , vol.9 , pp. 95-124
    • Haraux, A.1    Jendoubi, M.A.2
  • 122
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, Berlin
    • Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes Math. Vol. 840 (1981), Springer, Berlin
    • (1981) Lecture Notes Math. , vol.840
    • Henry, D.1
  • 123
    • 67649325545 scopus 로고
    • Perturbations of the boundary for boundary value problems of partial differential equations
    • ATS
    • Henry D. Perturbations of the boundary for boundary value problems of partial differential equations. Sem. Brazileiro Anal. 22 (1985), ATS
    • (1985) Sem. Brazileiro Anal. , vol.22
    • Henry, D.1
  • 124
    • 46549093257 scopus 로고
    • Some infinite dimensional Morse-Smale systems defined by parabolic differential equations
    • Henry D. Some infinite dimensional Morse-Smale systems defined by parabolic differential equations. J. Differential Equations 59 (1985) 165-205
    • (1985) J. Differential Equations , vol.59 , pp. 165-205
    • Henry, D.1
  • 125
    • 0042478296 scopus 로고
    • Generic properties of equilibrium solutions by perturbations of the boundary
    • Dynamics of Infinite Dimensional Systems, Springer, Berlin
    • Henry D. Generic properties of equilibrium solutions by perturbations of the boundary. Dynamics of Infinite Dimensional Systems. NATO ASI Ser. F Vol. 37 (1987), Springer, Berlin 129-139
    • (1987) NATO ASI Ser. F , vol.37 , pp. 129-139
    • Henry, D.1
  • 126
    • 0003347424 scopus 로고
    • Dimension Theory
    • Princeton Univ. Press, Princeton, NJ
    • Hurewicz W., and Wallman H. Dimension Theory. Princeton Math. Ser. Vol. 4 (1941), Princeton Univ. Press, Princeton, NJ
    • (1941) Princeton Math. Ser. , vol.4
    • Hurewicz, W.1    Wallman, H.2
  • 127
    • 85012651022 scopus 로고
    • Local decay of solutions for symmetric hyperbolic systems with dissipative and coercive boundary conditions in exterior domains
    • Iwasaki N. Local decay of solutions for symmetric hyperbolic systems with dissipative and coercive boundary conditions in exterior domains. Publ. Res. Inst. Math. Sci., Kyoto Univ. 5 (1969) 193-218
    • (1969) Publ. Res. Inst. Math. Sci., Kyoto Univ. , vol.5 , pp. 193-218
    • Iwasaki, N.1
  • 128
    • 0000171235 scopus 로고
    • Explicit construction of an inertial manifold for a reaction diffusion equation
    • Jolly M. Explicit construction of an inertial manifold for a reaction diffusion equation. J. Differential Equations 78 (1989) 220-261
    • (1989) J. Differential Equations , vol.78 , pp. 220-261
    • Jolly, M.1
  • 129
    • 0000646281 scopus 로고
    • Upper bounds on the number of determining modes, nodes, and volume elements for the Navier-Stokes equations
    • Jones D., and Titi E. Upper bounds on the number of determining modes, nodes, and volume elements for the Navier-Stokes equations. Indiana Math. J. 42 (1993) 875-887
    • (1993) Indiana Math. J. , vol.42 , pp. 875-887
    • Jones, D.1    Titi, E.2
  • 130
    • 0037953627 scopus 로고
    • Minimal compact global attractor for a damped wave equation
    • Kapitanski L. Minimal compact global attractor for a damped wave equation. Comm. Partial Differential Equations 20 (1995) 1303-1323
    • (1995) Comm. Partial Differential Equations , vol.20 , pp. 1303-1323
    • Kapitanski, L.1
  • 131
    • 0347238976 scopus 로고
    • A regular approach to a problem on the attractors of singularly perturbed equations
    • Kostin I.N. A regular approach to a problem on the attractors of singularly perturbed equations. Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 181 (1990) 93-131
    • (1990) Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova , vol.181 , pp. 93-131
    • Kostin, I.N.1
  • 132
    • 0010120014 scopus 로고
    • A regular approach to a problem on the attractors of singularly perturbed equations
    • English translation:
    • English translation:. Kostin I.N. A regular approach to a problem on the attractors of singularly perturbed equations. J. Soviet. Math. 62 (1992) 2664-2689
    • (1992) J. Soviet. Math. , vol.62 , pp. 2664-2689
    • Kostin, I.N.1
  • 133
    • 0346275724 scopus 로고
    • Lower semicontinuity of a non-hyperbolic attractor
    • Kostin I.N. Lower semicontinuity of a non-hyperbolic attractor. J. Lond. Math. Soc II 52 (1995) 568-582
    • (1995) J. Lond. Math. Soc II , vol.52 , pp. 568-582
    • Kostin, I.N.1
  • 134
    • 0003391813 scopus 로고
    • Academic Press, New York
    • Kuratowski K. Topology (1966), Academic Press, New York
    • (1966) Topology
    • Kuratowski, K.1
  • 135
    • 0001989779 scopus 로고
    • A dynamical system generated by the Navier-Stokes equations
    • Ladyzhenskaya O.A. A dynamical system generated by the Navier-Stokes equations. Zap. Nauch. Sem. LOMI 27 (1972) 91-114
    • (1972) Zap. Nauch. Sem. LOMI , vol.27 , pp. 91-114
    • Ladyzhenskaya, O.A.1
  • 136
    • 34250401659 scopus 로고
    • A dynamical system generated by the Navier-Stokes equations
    • English translation:
    • English translation:. Ladyzhenskaya O.A. A dynamical system generated by the Navier-Stokes equations. J. Soviet Math. 3 (1975) 458-479
    • (1975) J. Soviet Math. , vol.3 , pp. 458-479
    • Ladyzhenskaya, O.A.1
  • 137
    • 0006444781 scopus 로고
    • Dynamical system generated by the Navier-Stokes equations
    • Ladyzhenskaya O.A. Dynamical system generated by the Navier-Stokes equations. Soviet Phys. Dokl. 17 (1973) 647-649
    • (1973) Soviet Phys. Dokl. , vol.17 , pp. 647-649
    • Ladyzhenskaya, O.A.1
  • 138
    • 0001226227 scopus 로고
    • On the finite dimensionality of bounded invariant sets for the Navier-Stokes system and other dissipative systems
    • Ladyzhenskaya O.A. On the finite dimensionality of bounded invariant sets for the Navier-Stokes system and other dissipative systems. Zap. Nauchn. Semin. Leningrad Otd. Mat. Inst. Steklova 115 (1982) 137-155
    • (1982) Zap. Nauchn. Semin. Leningrad Otd. Mat. Inst. Steklova , vol.115 , pp. 137-155
    • Ladyzhenskaya, O.A.1
  • 139
    • 0000375959 scopus 로고
    • On the finite dimensionality of bounded invariant sets for the Navier-Stokes system and other dissipative systems
    • English translation:
    • English translation:. Ladyzhenskaya O.A. On the finite dimensionality of bounded invariant sets for the Navier-Stokes system and other dissipative systems. J. Soviet Math. 28 (1985) 714-726
    • (1985) J. Soviet Math. , vol.28 , pp. 714-726
    • Ladyzhenskaya, O.A.1
  • 141
    • 0348066060 scopus 로고
    • On the determination of minimal global attractors for the Navier-Stokes and other partial differential equations
    • Ladyzhenskaya O. On the determination of minimal global attractors for the Navier-Stokes and other partial differential equations. Russian Math. Surveys 42 (1987) 27-73
    • (1987) Russian Math. Surveys , vol.42 , pp. 27-73
    • Ladyzhenskaya, O.1
  • 142
    • 0039990605 scopus 로고
    • Estimates of the fractal dimension and of the number of deterministic modes for invariant sets of dynamical systems
    • Ladyzhenskaya O.A. Estimates of the fractal dimension and of the number of deterministic modes for invariant sets of dynamical systems. Zap. Nauchn. Semin. Leningrad Otd. Mat. Inst. Steklova 163 (1987) 105-129
    • (1987) Zap. Nauchn. Semin. Leningrad Otd. Mat. Inst. Steklova , vol.163 , pp. 105-129
    • Ladyzhenskaya, O.A.1
  • 143
    • 33747282844 scopus 로고
    • Estimates of the fractal dimension and of the number of deterministic modes for invariant sets of dynamical systems
    • English translation:
    • English translation:. Ladyzhenskaya O.A. Estimates of the fractal dimension and of the number of deterministic modes for invariant sets of dynamical systems. J. Soviet Math. 49 (1990) 1186-1201
    • (1990) J. Soviet Math. , vol.49 , pp. 1186-1201
    • Ladyzhenskaya, O.A.1
  • 144
    • 0000934645 scopus 로고
    • Some complements and corrections to my papers on the theory of attractors for abstract semigroups
    • Ladyzhenskaya O. Some complements and corrections to my papers on the theory of attractors for abstract semigroups. Zap. Nauchn. Semin. Leningrad Otd. Mat. Inst. Steklova 182 (1990) 102-112
    • (1990) Zap. Nauchn. Semin. Leningrad Otd. Mat. Inst. Steklova , vol.182 , pp. 102-112
    • Ladyzhenskaya, O.1
  • 145
    • 0042518783 scopus 로고
    • Some complements and corrections to my papers on the theory of attractors for abstract semigroups
    • English translation:
    • English translation:. Ladyzhenskaya O. Some complements and corrections to my papers on the theory of attractors for abstract semigroups. J. Soviet Math. 62 (1992) 2789-2794
    • (1992) J. Soviet Math. , vol.62 , pp. 2789-2794
    • Ladyzhenskaya, O.1
  • 147
    • 0003363086 scopus 로고
    • The Stability of Dynamical Systems
    • SIAM, Philadelphia, PA
    • LaSalle J.P. The Stability of Dynamical Systems. CBMS Regional Conference Ser. Vol. 25 (1976), SIAM, Philadelphia, PA
    • (1976) CBMS Regional Conference Ser. , vol.25
    • LaSalle, J.P.1
  • 149
    • 0040911560 scopus 로고
    • On a nonlinear delay equation
    • Levin J., and Nohel J. On a nonlinear delay equation. J. Math. Anal. Appl. 8 (1964) 31-44
    • (1964) J. Math. Anal. Appl. , vol.8 , pp. 31-44
    • Levin, J.1    Nohel, J.2
  • 150
    • 0001455091 scopus 로고
    • Transformation theory of nonlinear differential equations of the second order
    • Levinson N. Transformation theory of nonlinear differential equations of the second order. Ann. Math. 45 (1944) 724-737
    • (1944) Ann. Math. , vol.45 , pp. 724-737
    • Levinson, N.1
  • 151
    • 0003366108 scopus 로고
    • Une propriété topologique des sous-ensembles analytiques réels
    • Equations aux Dérivées Partielles (Paris, 1962)
    • Lojasiewicz S. Une propriété topologique des sous-ensembles analytiques réels. Equations aux Dérivées Partielles (Paris, 1962). Colloque International du CNRS Vol. 117 (1963)
    • (1963) Colloque International du CNRS , vol.117
    • Lojasiewicz, S.1
  • 152
    • 84974178842 scopus 로고
    • Compact attractor for a nonlinear wave equation with critical exponent
    • Lopes O. Compact attractor for a nonlinear wave equation with critical exponent. Proc. Roy. Soc. Edin-burgh 115 (1990) 61-64
    • (1990) Proc. Roy. Soc. Edin-burgh , vol.115 , pp. 61-64
    • Lopes, O.1
  • 153
    • 0005750037 scopus 로고
    • Negatively invariant sets of compact maps and an extension of a theorem of Cartwright
    • Mallet-Paret J. Negatively invariant sets of compact maps and an extension of a theorem of Cartwright. J. Differential Equations 22 (1976) 331-348
    • (1976) J. Differential Equations , vol.22 , pp. 331-348
    • Mallet-Paret, J.1
  • 154
    • 84968508885 scopus 로고
    • Inertial manifolds for reaction diffusion equations
    • Mallet-Paret J., and Sell G. Inertial manifolds for reaction diffusion equations. J. Amer. Math. Soc. 1 (1988) 805-866
    • (1988) J. Amer. Math. Soc. , vol.1 , pp. 805-866
    • Mallet-Paret, J.1    Sell, G.2
  • 155
    • 0003290175 scopus 로고
    • On the dimension of the compact invariant sets of certain non-linear maps
    • Dynamical Systems and Turbulence, Proc. Symp. Coventry. 1980
    • Mané R. On the dimension of the compact invariant sets of certain non-linear maps. Dynamical Systems and Turbulence, Proc. Symp. Coventry. 1980. Lecture Notes in Math. Vol. 898 (1981) 230-242
    • (1981) Lecture Notes in Math. , vol.898 , pp. 230-242
    • Mané, R.1
  • 156
    • 0011399737 scopus 로고
    • Some properties of α-condensing maps
    • Massatt P. Some properties of α-condensing maps. Ann. Pura Appl. 125 (1980) 101-115
    • (1980) Ann. Pura Appl. , vol.125 , pp. 101-115
    • Massatt, P.1
  • 157
    • 33749319241 scopus 로고
    • Attractivity properties of a-contractions
    • Massatt P. Attractivity properties of a-contractions. J. Differential Equations 48 (1983) 326-333
    • (1983) J. Differential Equations , vol.48 , pp. 326-333
    • Massatt, P.1
  • 158
    • 0000487658 scopus 로고
    • Limiting behavior for strongly damped nonlinear wave equations
    • Massatt P. Limiting behavior for strongly damped nonlinear wave equations. J. Differential Equations 48 (1983) 334-349
    • (1983) J. Differential Equations , vol.48 , pp. 334-349
    • Massatt, P.1
  • 160
    • 0000657925 scopus 로고
    • Nonincrease of lap number of a solution for a one-dimensional semilinear parabolic equation
    • Matano H. Nonincrease of lap number of a solution for a one-dimensional semilinear parabolic equation. J. Fac. Sci. Univ. Kyoto 30 (1982) 401-441
    • (1982) J. Fac. Sci. Univ. Kyoto , vol.30 , pp. 401-441
    • Matano, H.1
  • 162
    • 23444462190 scopus 로고
    • On unstable attractors
    • Mendelson P. On unstable attractors. Bol. Soc. Mat. Mex. 5 (1960) 270-276
    • (1960) Bol. Soc. Mat. Mex. , vol.5 , pp. 270-276
    • Mendelson, P.1
  • 163
    • 67649328063 scopus 로고    scopus 로고
    • ∞-estimates and attractors for parabolic systems on unbounded domains
    • International Conference on Differential Equations. Fiedler B. (Ed), World Scientific, Singapore
    • ∞-estimates and attractors for parabolic systems on unbounded domains. In: Fiedler B. (Ed). International Conference on Differential Equations. Proceedings of the Conference, Equadiff. 99, Berlin Vol. 1 (2000), World Scientific, Singapore 641-646
    • (2000) Proceedings of the Conference, Equadiff. 99, Berlin , vol.1 , pp. 641-646
    • Mielke, A.1
  • 164
    • 67649370945 scopus 로고    scopus 로고
    • The Ginzburg-Landau equation in its role as a modulation equation
    • Fiedler B. (Ed), Elsevier, Amsterdam
    • Mielke A. The Ginzburg-Landau equation in its role as a modulation equation. In: Fiedler B. (Ed). Handbook for Dynamical Systems Vol. 2 (2002), Elsevier, Amsterdam 759-834
    • (2002) Handbook for Dynamical Systems , vol.2 , pp. 759-834
    • Mielke, A.1
  • 165
    • 0000454926 scopus 로고
    • Attractors for modulation equations on unbounded domains -existence and comparison
    • Mielke A., and Schneider G. Attractors for modulation equations on unbounded domains -existence and comparison. Nonlinearity 8 (1995) 743-768
    • (1995) Nonlinearity , vol.8 , pp. 743-768
    • Mielke, A.1    Schneider, G.2
  • 166
    • 50549220483 scopus 로고
    • On asymptotic stability of almost periodic systems
    • Miller R.K. On asymptotic stability of almost periodic systems. J. Differential Equations 1 (1965) 234-239
    • (1965) J. Differential Equations , vol.1 , pp. 234-239
    • Miller, R.K.1
  • 167
    • 67649346541 scopus 로고
    • Topological dynamics and its relation to integral equations and nonautonomous systems
    • Academic Press, New York
    • Miller R.K., and Sell G. Topological dynamics and its relation to integral equations and nonautonomous systems. Dynamical Systems Vol. 1 (1976), Academic Press, New York 223-249
    • (1976) Dynamical Systems , vol.1 , pp. 223-249
    • Miller, R.K.1    Sell, G.2
  • 168
    • 34250112778 scopus 로고
    • On the concept of attractors
    • Milnor J. On the concept of attractors. Commun. Math. Phys. 99 (1985) 177-195
    • (1985) Commun. Math. Phys. , vol.99 , pp. 177-195
    • Milnor, J.1
  • 169
    • 0001996785 scopus 로고
    • On the concept of attractor: correction and remarks
    • Comments
    • Comments. On the concept of attractor: correction and remarks. Commun. Math. Phys. 102 (1985) 517-519
    • (1985) Commun. Math. Phys. , vol.102 , pp. 517-519
  • 170
    • 67649370946 scopus 로고    scopus 로고
    • Conley index
    • Fiedler B. (Ed), Elsevier, Amsterdam
    • Mischaikow K., and Mrozek M. Conley index. In: Fiedler B. (Ed). Handbook for Dynamical Systems Vol. 2 (2002), Elsevier, Amsterdam 393-460
    • (2002) Handbook for Dynamical Systems , vol.2 , pp. 393-460
    • Mischaikow, K.1    Mrozek, M.2
  • 172
    • 84966209285 scopus 로고
    • On the inverse of Mañé's projection
    • Movahedi-Lankarani H. On the inverse of Mañé's projection. Proc. Amer. Math. Soc. 116 (1992) 555-560
    • (1992) Proc. Amer. Math. Soc. , vol.116 , pp. 555-560
    • Movahedi-Lankarani, H.1
  • 173
    • 0004263512 scopus 로고    scopus 로고
    • Attractors for non-compact semigroups via energy equations
    • Moise I., Rosa R., and Wang X. Attractors for non-compact semigroups via energy equations. Nonlinearity 11 (1998) 1369-1393
    • (1998) Nonlinearity , vol.11 , pp. 1369-1393
    • Moise, I.1    Rosa, R.2    Wang, X.3
  • 174
    • 45149143498 scopus 로고
    • The singular limit of semilinear damped equations
    • Mora X., and Solà-Morales J. The singular limit of semilinear damped equations. J. Differential Equations 78 (1989) 262-307
    • (1989) J. Differential Equations , vol.78 , pp. 262-307
    • Mora, X.1    Solà-Morales, J.2
  • 175
    • 84941507534 scopus 로고
    • Gestaltaussagen über Lösungen parabolischer Differentialgleichungen
    • Nickel K. Gestaltaussagen über Lösungen parabolischer Differentialgleichungen. J. Reine Angew. Math. 211 (1962) 78-94
    • (1962) J. Reine Angew. Math. , vol.211 , pp. 78-94
    • Nickel, K.1
  • 176
    • 0001035921 scopus 로고
    • Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
    • Nicolaenko B., Scheurer B., and Temam R. Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors. Phys. D 16 (1985) 155-183
    • (1985) Phys. D , vol.16 , pp. 155-183
    • Nicolaenko, B.1    Scheurer, B.2    Temam, R.3
  • 177
    • 0022773959 scopus 로고
    • Low-dimensional chaos in a driven damped nonlinear Schrödinger equation
    • Nozaki K., and Bekki N. Low-dimensional chaos in a driven damped nonlinear Schrödinger equation. Phys. D 21 (1986) 381-393
    • (1986) Phys. D , vol.21 , pp. 381-393
    • Nozaki, K.1    Bekki, N.2
  • 178
    • 84972570025 scopus 로고
    • The radius of the essential spectrum
    • Nussbaum R. The radius of the essential spectrum. Duke Math. J. 38 (1970) 473-488
    • (1970) Duke Math. J. , vol.38 , pp. 473-488
    • Nussbaum, R.1
  • 179
    • 84966202985 scopus 로고
    • Some asymptotic fixed points
    • Nussbaum R. Some asymptotic fixed points. Trans. Amer. Math. Soc. 171 (1972) 349-375
    • (1972) Trans. Amer. Math. Soc. , vol.171 , pp. 349-375
    • Nussbaum, R.1
  • 180
    • 0012604866 scopus 로고
    • Periodic solutions of analytic functional differential equations are analytic
    • Nussbaum R. Periodic solutions of analytic functional differential equations are analytic. Michigan Math. J. 20 (1973) 249-255
    • (1973) Michigan Math. J. , vol.20 , pp. 249-255
    • Nussbaum, R.1
  • 181
    • 67649336781 scopus 로고    scopus 로고
    • Functional differential equations
    • Fiedler B. (Ed), Elsevier, Amsterdam
    • Nussbaum R. Functional differential equations. In: Fiedler B. (Ed). Handbook for Dynamical Systems Vol. 2 (2002), Elsevier, Amsterdam 461-499
    • (2002) Handbook for Dynamical Systems , vol.2 , pp. 461-499
    • Nussbaum, R.1
  • 183
    • 0001908166 scopus 로고    scopus 로고
    • Analyticity of the attractor and the number of determining nodes for a weakly damped driven nonlinear Schrödinger equation
    • Oliver M., and Titi E. Analyticity of the attractor and the number of determining nodes for a weakly damped driven nonlinear Schrödinger equation. Indiana Univ. Math. J. 47 (1998) 49-73
    • (1998) Indiana Univ. Math. J. , vol.47 , pp. 49-73
    • Oliver, M.1    Titi, E.2
  • 184
    • 49849128478 scopus 로고
    • On Morse-Smale dynamical systems
    • Palis J. On Morse-Smale dynamical systems. Topology 8 (1969) 385-405
    • (1969) Topology , vol.8 , pp. 385-405
    • Palis, J.1
  • 185
    • 0001328790 scopus 로고
    • Structural stability theorems
    • Amer. Math. Soc., Providence, RI
    • Palis J., and Smale S. Structural stability theorems. Global Analysis, Proc. Symp. Pure Math. Vol. 14 (1970), Amer. Math. Soc., Providence, RI
    • (1970) Global Analysis, Proc. Symp. Pure Math. , vol.14
    • Palis, J.1    Smale, S.2
  • 187
    • 0003316678 scopus 로고
    • Semigroups of Linear Operators and Applications to Partial Differential Equations
    • Springer, New York
    • Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Appl. Math. Sci. Vol. 44 (1983), Springer, New York
    • (1983) Appl. Math. Sci. , vol.44
    • Pazy, A.1
  • 189
    • 84972538906 scopus 로고
    • Transversal and nontransversal intersection of stable and unstable manifolds of reaction diffu-sion equations on symmetric domains
    • Poláčik P. Transversal and nontransversal intersection of stable and unstable manifolds of reaction diffu-sion equations on symmetric domains. Differential Integral Equations 7 (1994) 1527-1545
    • (1994) Differential Integral Equations , vol.7 , pp. 1527-1545
    • Poláčik, P.1
  • 190
    • 33745176729 scopus 로고    scopus 로고
    • Parabolic equations: asymptotic behavior and dynamics on invariant manifolds
    • Fiedler B. (Ed), Elsevier, Amsterdam
    • Poláčik P. Parabolic equations: asymptotic behavior and dynamics on invariant manifolds. In: Fiedler B. (Ed). Handbook for Dynamical Systems Vol. 2 (2002), Elsevier, Amsterdam 835-883
    • (2002) Handbook for Dynamical Systems , vol.2 , pp. 835-883
    • Poláčik, P.1
  • 191
    • 16144369367 scopus 로고    scopus 로고
    • Nonconvergent bounded trajectories in semilinear heat equations
    • Poláčik P., and Rybakowski K. Nonconvergent bounded trajectories in semilinear heat equations. J. Dif-ferential Equations 124 (1996) 472-494
    • (1996) J. Dif-ferential Equations , vol.124 , pp. 472-494
    • Poláčik, P.1    Rybakowski, K.2
  • 192
    • 0025725569 scopus 로고
    • Time analyticity and Gevrey regularity for solutions of a class of dissipative partial differ-ential equations
    • Promislow K. Time analyticity and Gevrey regularity for solutions of a class of dissipative partial differ-ential equations. Nonlinear Anal. 16 (1991) 959-980
    • (1991) Nonlinear Anal. , vol.16 , pp. 959-980
    • Promislow, K.1
  • 194
    • 0001278064 scopus 로고
    • Dynamics of Partial Differential Equations on Thin Domains
    • Springer, Berlin
    • Raugel G. Dynamics of Partial Differential Equations on Thin Domains. CIME Course, Montecatini Terme, Lecture Notes in Math. Vol. 1609 (1995), Springer, Berlin 208-315
    • (1995) CIME Course, Montecatini Terme, Lecture Notes in Math. , vol.1609 , pp. 208-315
    • Raugel, G.1
  • 195
    • 67649346543 scopus 로고    scopus 로고
    • Singularly perturbed hyperbolic equations revisited
    • International Conference on Differential Equations. Fiedler B. (Ed), World Scientific, Singapore
    • Raugel G. Singularly perturbed hyperbolic equations revisited. In: Fiedler B. (Ed). International Conference on Differential Equations. Proceedings of the Conference, Equadiff. 99, Berlin Vol. 1 (2000), World Scientific, Singapore 647-652
    • (2000) Proceedings of the Conference, Equadiff. 99, Berlin , vol.1 , pp. 647-652
    • Raugel, G.1
  • 197
    • 0000242980 scopus 로고    scopus 로고
    • Global attractors: topology and finite-dimensional dynamics
    • Robinson J.C. Global attractors: topology and finite-dimensional dynamics. J. Dynamics Differential Equations 11 (1999) 557-581
    • (1999) J. Dynamics Differential Equations , vol.11 , pp. 557-581
    • Robinson, J.C.1
  • 198
    • 0001032545 scopus 로고
    • Properties of the attractor of a scalar parabolic PDE
    • Rocha C. Properties of the attractor of a scalar parabolic PDE. J. Dynamics Differential Equations 3 (1991) 575-591
    • (1991) J. Dynamics Differential Equations , vol.3 , pp. 575-591
    • Rocha, C.1
  • 199
    • 0000687761 scopus 로고
    • Unique continuation for weak solutions of the wave equation plus a potential
    • Ruiz A. Unique continuation for weak solutions of the wave equation plus a potential. J. Math. Pures Appl. 71 (1992) 455-467
    • (1992) J. Math. Pures Appl. , vol.71 , pp. 455-467
    • Ruiz, A.1
  • 200
    • 84968469711 scopus 로고
    • On the homotopy index for infinite-dimensional semi-flows
    • Rybakowski K.P. On the homotopy index for infinite-dimensional semi-flows. TAMS 269 (1982) 351-383
    • (1982) TAMS , vol.269 , pp. 351-383
    • Rybakowski, K.P.1
  • 201
    • 0005906189 scopus 로고
    • The Morse index repeller-attractor pairs and the connection index for semiflows on noncompact spaces
    • Rybakowski K.P. The Morse index repeller-attractor pairs and the connection index for semiflows on noncompact spaces. J. Differential Equations 47 (1983) 66-98
    • (1983) J. Differential Equations , vol.47 , pp. 66-98
    • Rybakowski, K.P.1
  • 203
    • 84968510092 scopus 로고
    • Nonautonomous differential equations and topological dynamics. I: The basic theory
    • Sell G.R. Nonautonomous differential equations and topological dynamics. I: The basic theory. Trans. Amer. Math. Soc. 127 (1967) 241-262
    • (1967) Trans. Amer. Math. Soc. , vol.127 , pp. 241-262
    • Sell, G.R.1
  • 206
    • 0000137102 scopus 로고
    • Asymptotic s for a class of nonlinear evolution equations, with applications to geometric prob-lems
    • Simon L. Asymptotic s for a class of nonlinear evolution equations, with applications to geometric prob-lems. Ann. of Math. 118 (1983) 525-571
    • (1983) Ann. of Math. , vol.118 , pp. 525-571
    • Simon, L.1
  • 207
    • 0343247398 scopus 로고
    • Generic properties of steady state solutions
    • Smoller J., and Wasserman A. Generic properties of steady state solutions. J. Differential Equation 52 (1984) 423-438
    • (1984) J. Differential Equation , vol.52 , pp. 423-438
    • Smoller, J.1    Wasserman, A.2
  • 210
    • 0001746066 scopus 로고
    • Entropy and the Hausdorjf dimension for infinite-dimensional dynamical systems
    • Thieullen P. Entropy and the Hausdorjf dimension for infinite-dimensional dynamical systems. J. Dynam-ics Differential Equations 4 (1992) 127-159
    • (1992) J. Dynam-ics Differential Equations , vol.4 , pp. 127-159
    • Thieullen, P.1
  • 212
    • 0000767629 scopus 로고
    • Sur la théorie mathématique des phénomènes héréditaires
    • Volterra V. Sur la théorie mathématique des phénomènes héréditaires. J. Math. Pures Appl. 7 (1928) 249-298
    • (1928) J. Math. Pures Appl. , vol.7 , pp. 249-298
    • Volterra, V.1
  • 214
    • 84971947724 scopus 로고
    • Compactness of bounded trajectories of dynamical systems in infinite dimensional spaces
    • Webb G.F. Compactness of bounded trajectories of dynamical systems in infinite dimensional spaces. Proc. Roy. Soc. Edinburgh 84 (1979) 19-34
    • (1979) Proc. Roy. Soc. Edinburgh , vol.84 , pp. 19-34
    • Webb, G.F.1
  • 215
    • 0000479863 scopus 로고
    • A bifurcation problem for a nonlinear hyperbolic partial differential equation
    • Webb G.F. A bifurcation problem for a nonlinear hyperbolic partial differential equation. SIAM J. Math. Anal. 10 (1979) 922-932
    • (1979) SIAM J. Math. Anal. , vol.10 , pp. 922-932
    • Webb, G.F.1
  • 216
    • 0000999961 scopus 로고
    • Existence and asymptotic behavior for a strongly damped nonlinear wave equation
    • Webb G.F. Existence and asymptotic behavior for a strongly damped nonlinear wave equation. Canad. J. Math. 32 (1980) 631-643
    • (1980) Canad. J. Math. , vol.32 , pp. 631-643
    • Webb, G.F.1
  • 217
    • 84972564130 scopus 로고
    • Invariant manifolds of nonlinear operators
    • Wells J.C. Invariant manifolds of nonlinear operators. Pacific J. Math. 62 (1976) 285-293
    • (1976) Pacific J. Math. , vol.62 , pp. 285-293
    • Wells, J.C.1
  • 218
    • 34249760077 scopus 로고
    • Existence and continuity of the attractor for a singularly perturbed hyperbolic equation
    • Witt I. Existence and continuity of the attractor for a singularly perturbed hyperbolic equation. J. Dy-namics Differential Equations 7 (1995) 591-639
    • (1995) J. Dy-namics Differential Equations , vol.7 , pp. 591-639
    • Witt, I.1
  • 221
    • 0001883857 scopus 로고
    • Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable
    • Zelenyak T.J. Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable. Differential Equations 4 (1968) 17-22
    • (1968) Differential Equations , vol.4 , pp. 17-22
    • Zelenyak, T.J.1
  • 223
    • 0041172086 scopus 로고
    • The mixed problem for hyperbolic equations with a small parameter
    • Zlámal M. The mixed problem for hyperbolic equations with a small parameter. Czechosl. Math. J. 10 (1960) 83-122
    • (1960) Czechosl. Math. J. , vol.10 , pp. 83-122
    • Zlámal, M.1
  • 224
    • 0000976025 scopus 로고
    • Exponential decay for the semilinear wave equation with locally distributed damping
    • Zuazua E. Exponential decay for the semilinear wave equation with locally distributed damping. Com-mun. Partial Differential Equations 15 (1990) 205-235
    • (1990) Com-mun. Partial Differential Equations , vol.15 , pp. 205-235
    • Zuazua, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.