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Volumn 2, Issue , 2002, Pages 835-883

Chapter 16 Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds

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EID: 33745176729     PISSN: 1874575X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-575X(02)80037-6     Document Type: Chapter
Times cited : (75)

References (213)
  • 1
    • 84972506464 scopus 로고
    • Liapunov operators and stabilization in strongly order-preserving dynamical systems
    • Alikakos N.D., and Hess P. Liapunov operators and stabilization in strongly order-preserving dynamical systems. Differential Integral Equations 4 (1991) 15-24
    • (1991) Differential Integral Equations , vol.4 , pp. 15-24
    • Alikakos, N.D.1    Hess, P.2
  • 2
    • 0001458211 scopus 로고
    • Discrete order preserving semigroups and stability for periodic parabolic differential equations
    • Alikakos N.D., Hess P., and Matano H. Discrete order preserving semigroups and stability for periodic parabolic differential equations. J. Differential Equations 82 (1989) 322-341
    • (1989) J. Differential Equations , vol.82 , pp. 322-341
    • Alikakos, N.D.1    Hess, P.2    Matano, H.3
  • 3
    • 0017014016 scopus 로고
    • Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces
    • Amann H. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 (1976) 620-709
    • (1976) SIAM Rev. , vol.18 , pp. 620-709
    • Amann, H.1
  • 4
    • 0002970101 scopus 로고
    • Global existence for semilinear parabolic systems
    • Amann H. Global existence for semilinear parabolic systems. J. Reine Angew. Math. 360 (1985) 47-83
    • (1985) J. Reine Angew. Math. , vol.360 , pp. 47-83
    • Amann, H.1
  • 5
    • 0000324117 scopus 로고
    • Quasilinear parabolic systems under nonlinear boundary conditions
    • Amann H. Quasilinear parabolic systems under nonlinear boundary conditions. Arch. Rational Mech. Anal. 92 (1986) 153-192
    • (1986) Arch. Rational Mech. Anal. , vol.92 , pp. 153-192
    • Amann, H.1
  • 7
    • 0000329412 scopus 로고
    • The Morse-Smale property for a semilinear parabolic equation
    • Angenent S. 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.1
  • 8
    • 84942222028 scopus 로고
    • The zeroset of a solution of a parabolic equation
    • Angenent S. The zeroset of a solution of a parabolic equation. J. Reine Angew. Math. 390 (1988) 79-96
    • (1988) J. Reine Angew. Math. , vol.390 , pp. 79-96
    • Angenent, S.1
  • 9
    • 0000720224 scopus 로고
    • Solutions of the 1-d porous medium equations are determined by their free boundary
    • Angenent S. Solutions of the 1-d porous medium equations are determined by their free boundary. J. London Math. Soc. 43 (1990) 339-353
    • (1990) J. London Math. Soc. , vol.43 , pp. 339-353
    • Angenent, S.1
  • 10
    • 0001315014 scopus 로고
    • Parabolic equations for curves on surfaces. II. intersection, blow-up and generalized solutions
    • Angenent S. Parabolic equations for curves on surfaces. II. intersection, blow-up and generalized solutions. Ann. of Math. 133 (1991) 171-215
    • (1991) Ann. of Math. , vol.133 , pp. 171-215
    • Angenent, S.1
  • 11
    • 33646918069 scopus 로고
    • The dynamics of rotating waves in scalar reaction diffusion equations
    • Angenent S., and Fiedler B. The dynamics of rotating waves in scalar reaction diffusion equations. Trans. Amer. Math. Soc. 307 2 (1988) 545-568
    • (1988) Trans. Amer. Math. Soc. , vol.307 , Issue.2 , pp. 545-568
    • Angenent, S.1    Fiedler, B.2
  • 14
    • 0002428935 scopus 로고
    • Symmetrization properties of parabolic equations in symmetric domains
    • Babin A.V. Symmetrization properties of parabolic equations in symmetric domains. J. Dynamics Differential Equations 6 4 (1994) 639-658
    • (1994) J. Dynamics Differential Equations , vol.6 , Issue.4 , pp. 639-658
    • Babin, A.V.1
  • 15
    • 0002487191 scopus 로고
    • Symmetry of instabilities for scalar equations in symmetric domains
    • Babin A.V. Symmetry of instabilities for scalar equations in symmetric domains. J. Differential Equations 123 1 (1995) 122-152
    • (1995) J. Differential Equations , vol.123 , Issue.1 , pp. 122-152
    • Babin, A.V.1
  • 16
    • 0033634626 scopus 로고    scopus 로고
    • Attractors of non-autonomous parabolic equations and their symmetry properties
    • Babin A.V., and Sell G.R. Attractors of non-autonomous parabolic equations and their symmetry properties. J. Differential Equations 160 1 (2000) 1-50
    • (2000) J. Differential Equations , vol.160 , Issue.1 , pp. 1-50
    • Babin, A.V.1    Sell, G.R.2
  • 17
    • 33748109655 scopus 로고    scopus 로고
    • Existence and persistence of invariant manifolds for semiflows in Banach space
    • Bates P.W., Lu K., and Zeng C. Existence and persistence of invariant manifolds for semiflows in Banach space. Mem. Amer. Math. Soc. 645 (1998) 1-129
    • (1998) Mem. Amer. Math. Soc. , vol.645 , pp. 1-129
    • Bates, P.W.1    Lu, K.2    Zeng, C.3
  • 20
    • 13844311748 scopus 로고
    • On the method of moving planes and the sliding method
    • Berestycki H., and Nirenberg L. On the method of moving planes and the sliding method. Bol. Soc. Brasil. Mat. (N.S.) 22 1 (1991) 1-37
    • (1991) Bol. Soc. Brasil. Mat. (N.S.) , vol.22 , Issue.1 , pp. 1-37
    • Berestycki, H.1    Nirenberg, L.2
  • 21
    • 84990602584 scopus 로고
    • The principal eigenvalue and maximum principle for second-order elliptic operators in general domains
    • Berestycki H., Nirenberg L., and Varadhan S.R.S. The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Comm. Pure Appl. Math. 47 1 (1994) 47-92
    • (1994) Comm. Pure Appl. Math. , vol.47 , Issue.1 , pp. 47-92
    • Berestycki, H.1    Nirenberg, L.2    Varadhan, S.R.S.3
  • 22
    • 0032135817 scopus 로고    scopus 로고
    • Large-time asymptotic equivalence for a class of nonautonomous semilinear parabolic equations
    • Bernfeld S.R., Hu Y.Y., and Vuillermot P. Large-time asymptotic equivalence for a class of nonautonomous semilinear parabolic equations. Bull. Sci. Math. 122 (1998) 337-368
    • (1998) Bull. Sci. Math. , vol.122 , pp. 337-368
    • Bernfeld, S.R.1    Hu, Y.Y.2    Vuillermot, P.3
  • 25
    • 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 3 (1990) 293-323
    • (1990) J. Dynamics Differential Equations , vol.2 , Issue.3 , pp. 293-323
    • Brunovský, P.1
  • 26
    • 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 1 (1989) 106-135
    • (1989) J. Differential Equations , vol.81 , Issue.1 , pp. 106-135
    • Brunovský, P.1    Fiedler, B.2
  • 27
    • 0001433697 scopus 로고
    • Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip
    • Brunovský P., Mora X., Poláčik P., and Solá-Morales J. Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Acta Math. Univ. Comenian. (N.S.) 60 2 (1991) 163-183
    • (1991) Acta Math. Univ. Comenian. (N.S.) , vol.60 , Issue.2 , pp. 163-183
    • Brunovský, P.1    Mora, X.2    Poláčik, P.3    Solá-Morales, J.4
  • 28
    • 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 6 (1997) 976-986
    • (1997) Z. Angew. Math. Phys. , vol.48 , Issue.6 , pp. 976-986
    • Brunovský, P.1    Poláčik, P.2
  • 29
    • 0001583347 scopus 로고
    • Convergence in general periodic parabolic equations in one space dimension
    • Brunovský P., Poláčik P., and Sandstede B. Convergence in general periodic parabolic equations in one space dimension. Nonlinear Analysis TMA 18 (1992) 209-215
    • (1992) Nonlinear Analysis TMA , vol.18 , pp. 209-215
    • Brunovský, P.1    Poláčik, P.2    Sandstede, B.3
  • 31
    • 0001731871 scopus 로고
    • Instability results for reaction diffusion equations with Neumann boundary conditions
    • Casten R.C., and Holland C.J. Instability results for reaction diffusion equations with Neumann boundary conditions. J. Differential Equations 27 (1978) 266-273
    • (1978) J. Differential Equations , vol.27 , pp. 266-273
    • Casten, R.C.1    Holland, C.J.2
  • 32
    • 0001909969 scopus 로고
    • Symmetry breaking for a class of semilinear elliptic problems
    • Cerami G. Symmetry breaking for a class of semilinear elliptic problems. J. Nonlinear Anal. TMA 10 (1986) 1-14
    • (1986) J. Nonlinear Anal. TMA , vol.10 , pp. 1-14
    • Cerami, G.1
  • 33
    • 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
  • 34
    • 38249028889 scopus 로고
    • Analysis of a convective reaction-diffusion equation
    • Chen T.-F., Levine H.A., and Sacks P.E. Analysis of a convective reaction-diffusion equation. Nonlinear Anal. 12 12 (1988) 1349-1370
    • (1988) Nonlinear Anal. , vol.12 , Issue.12 , pp. 1349-1370
    • Chen, T.-F.1    Levine, H.A.2    Sacks, P.E.3
  • 35
    • 0344408780 scopus 로고
    • Uniqueness of the ω-limit point of solutions of a semilinear heat equation on the circle
    • Chen X.-Y. Uniqueness of the ω-limit point of solutions of a semilinear heat equation on the circle. Proc. Japan Acad. Ser. A Math. Sci. 62 9 (1986) 335-337
    • (1986) Proc. Japan Acad. Ser. A Math. Sci. , vol.62 , Issue.9 , pp. 335-337
    • Chen, X.-Y.1
  • 36
    • 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 4 (1998) 603-630
    • (1998) Math. Ann. , vol.311 , Issue.4 , pp. 603-630
    • Chen, X.-Y.1
  • 37
    • 50849145650 scopus 로고
    • Convergence, asymptotic periodicity, and finite-point blow-up in one-dimensional semilinear heat equations
    • Chen X.-Y., and Matano H. Convergence, asymptotic periodicity, and finite-point blow-up in one-dimensional semilinear heat equations. J. Differential Equations 78 1 (1989) 160-190
    • (1989) J. Differential Equations , vol.78 , Issue.1 , pp. 160-190
    • Chen, X.-Y.1    Matano, H.2
  • 39
    • 0003287946 scopus 로고
    • Gradient-like structure and Morse decompositions for time-periodic one-dimensional parabolic equations
    • Chen X.-Y., and Poláčik P. Gradient-like structure and Morse decompositions for time-periodic one-dimensional parabolic equations. J. Dynamics Differential Equations 7 1 (1995) 73-107
    • (1995) J. Dynamics Differential Equations , vol.7 , Issue.1 , pp. 73-107
    • Chen, X.-Y.1    Poláčik, P.2
  • 40
    • 84969732524 scopus 로고    scopus 로고
    • Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball
    • Chen X.-Y., and Poláčik P. Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. J. Reine Angew. Math. 472 (1996) 17-51
    • (1996) J. Reine Angew. Math. , vol.472 , pp. 17-51
    • Chen, X.-Y.1    Poláčik, P.2
  • 41
    • 51249192264 scopus 로고
    • Eigenfunctions and nodal sets
    • Cheng S.Y. Eigenfunctions and nodal sets. Comment. Math. Helv. 51 1 (1976) 43-55
    • (1976) Comment. Math. Helv. , vol.51 , Issue.1 , pp. 43-55
    • Cheng, S.Y.1
  • 42
    • 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 2 (1988) 285-317
    • (1988) J. Differential Equations , vol.74 , Issue.2 , pp. 285-317
    • Chow, S.-N.1    Lu, K.2
  • 43
    • 0000770518 scopus 로고
    • Floquet theory for parabolic differential equations
    • Chow S.-N., Lu K., and Mallet-Paret J. Floquet theory for parabolic differential equations. J. Differential Equations 109 1 (1994) 147-200
    • (1994) J. Differential Equations , vol.109 , Issue.1 , pp. 147-200
    • Chow, S.-N.1    Lu, K.2    Mallet-Paret, J.3
  • 44
  • 45
    • 0003262604 scopus 로고
    • Isolated Invariant Sets and the Morse Index
    • Amer. Math. Soc., Providence, RI
    • Conley C. Isolated Invariant Sets and the Morse Index. CBMS Regional Conf. Ser. Math. Vol. 38 (1978), Amer. Math. Soc., Providence, RI
    • (1978) CBMS Regional Conf. Ser. Math. , vol.38
    • Conley, C.1
  • 46
    • 0000589157 scopus 로고
    • On nonradially symmetric bifurcation
    • Dancer E.N. On nonradially symmetric bifurcation. J. London Math. Soc. 20 2 (1979) 287-292
    • (1979) J. London Math. Soc. , vol.20 , Issue.2 , pp. 287-292
    • Dancer, E.N.1
  • 47
    • 0009157882 scopus 로고
    • On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients
    • (3)
    • (3). Dancer E.N. On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 4 (1991) 455-471
    • (1991) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.18 , Issue.4 , pp. 455-471
    • Dancer, E.N.1
  • 48
    • 84971725019 scopus 로고
    • Some notes on the method of moving planes
    • Dancer E.N. Some notes on the method of moving planes. Bull. Austral. Math. Soc. 46 3 (1992) 425-434
    • (1992) Bull. Austral. Math. Soc. , vol.46 , Issue.3 , pp. 425-434
    • Dancer, E.N.1
  • 49
    • 0001147857 scopus 로고
    • Stable subharmonic solutions in periodic reaction-diffusion equations
    • Dancer E.N., and Hess P. Stable subharmonic solutions in periodic reaction-diffusion equations. J. Differential Equations 108 1 (1994) 190-200
    • (1994) J. Differential Equations , vol.108 , Issue.1 , pp. 190-200
    • Dancer, E.N.1    Hess, P.2
  • 50
    • 3342986019 scopus 로고
    • The symmetry of positive solutions of periodic-parabolic problems
    • Dancer E.N., and Hess P. The symmetry of positive solutions of periodic-parabolic problems. J. Comput. Appl. Math. 52 1-3 (1994) 81-89
    • (1994) J. Comput. Appl. Math. , vol.52 , Issue.1-3 , pp. 81-89
    • Dancer, E.N.1    Hess, P.2
  • 51
    • 0033164310 scopus 로고    scopus 로고
    • Realization of vector fields and dynamics of spatially homogeneous parabolic equations
    • Dancer E.N., and Poláčik P. Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Mem. Amer. Math. Soc. 668 (1999) 1-82
    • (1999) Mem. Amer. Math. Soc. , vol.668 , pp. 1-82
    • Dancer, E.N.1    Poláčik, P.2
  • 55
    • 0002086916 scopus 로고    scopus 로고
    • The evolution of slow dispersal rates: a reaction-diffusion model
    • Dockery J., Hutson V., Mischaikow K., and Pernarowski M. The evolution of slow dispersal rates: a reaction-diffusion model. J. Math. Biol. 37 1 (1998) 61-83
    • (1998) J. Math. Biol. , vol.37 , Issue.1 , pp. 61-83
    • Dockery, J.1    Hutson, V.2    Mischaikow, K.3    Pernarowski, M.4
  • 56
    • 0000753322 scopus 로고
    • Realisation of ordinary differential equations by retarded functional differential equations in neighborhoods of equilibrium points
    • Faria T., and Magalhães L. Realisation of ordinary differential equations by retarded functional differential equations in neighborhoods of equilibrium points. Proc. Royal Soc. Edinburgh Sect. A 125 (1995) 759-770
    • (1995) Proc. Royal Soc. Edinburgh Sect. A , vol.125 , pp. 759-770
    • Faria, T.1    Magalhães, L.2
  • 57
    • 24544452205 scopus 로고    scopus 로고
    • Asymptotic analysis for a nonlinear parabolic equation on R
    • Preprint
    • E. Fašangová, Asymptotic analysis for a nonlinear parabolic equation on R, Preprint.
    • Fašangová, E.1
  • 58
    • 11744363608 scopus 로고
    • Convergence to an equilibrium for semilinear wave equations on unbounded intervals
    • Feireisl E. Convergence to an equilibrium for semilinear wave equations on unbounded intervals. Dynam. Systems Appl. 3 3 (1994) 423-434
    • (1994) Dynam. Systems Appl. , vol.3 , Issue.3 , pp. 423-434
    • Feireisl, E.1
  • 60
    • 0000749748 scopus 로고    scopus 로고
    • Convergence to a ground state as a threshold phenomenon in nonlinear parabolic equations
    • Feireisl E., and Petzeltová H. Convergence to a ground state as a threshold phenomenon in nonlinear parabolic equations. Differential Integral Equations 10 (1997) 181-196
    • (1997) Differential Integral Equations , vol.10 , pp. 181-196
    • Feireisl, E.1    Petzeltová, H.2
  • 61
    • 0012120695 scopus 로고    scopus 로고
    • Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on R
    • Feireisl E., and Poláčik P. Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on R. Adv. Differential Equations 5 (2000) 583-622
    • (2000) Adv. Differential Equations , vol.5 , pp. 583-622
    • Feireisl, E.1    Poláčik, P.2
  • 62
    • 0033096212 scopus 로고    scopus 로고
    • Convergence for degenerate parabolic equations
    • Feireisl E., and Simondon F. Convergence for degenerate parabolic equations. J. Differential Equations 152 2 (1999) 439-466
    • (1999) J. Differential Equations , vol.152 , Issue.2 , pp. 439-466
    • Feireisl, E.1    Simondon, F.2
  • 63
    • 0040342401 scopus 로고    scopus 로고
    • Convergence for degenerate parabolic equations in one dimension
    • Feireisl E., and Simondon F. Convergence for degenerate parabolic equations in one dimension. C. R. Acad. Sci. Paris Sér. I Math. 323 3 (1996) 251-255
    • (1996) C. R. Acad. Sci. Paris Sér. I Math. , vol.323 , Issue.3 , pp. 251-255
    • Feireisl, E.1    Simondon, F.2
  • 64
    • 0001356311 scopus 로고
    • Persistence and smoothness for invariant manifolds of flows
    • Fenichel N. Persistence and smoothness for invariant manifolds of flows. Indiana Univ. Math. J. 21 (1971) 193-226
    • (1971) Indiana Univ. Math. J. , vol.21 , pp. 193-226
    • Fenichel, N.1
  • 65
    • 0000618948 scopus 로고
    • Discrete Lyapunov functionals and ω-limit sets
    • Fiedler B. Discrete Lyapunov functionals and ω-limit sets. Math. Mod. Num. Anal. 23 (1989) 415-431
    • (1989) Math. Mod. Num. Anal. , vol.23 , pp. 415-431
    • Fiedler, B.1
  • 66
    • 0001794246 scopus 로고
    • Global attractors of one-dimensional parabolic equations: sixteen examples
    • Equadiff 8 (Bratislava, 1993)
    • Equadiff 8 (Bratislava, 1993). 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
  • 67
    • 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 4 (1989) 325-345
    • (1989) Arch. Rational Mech. Anal. , vol.107 , Issue.4 , pp. 325-345
    • Fiedler, B.1    Mallet-Paret, J.2
  • 68
    • 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 1-2 (1990) 167-192
    • (1990) Proc. Roy. Soc. Edinburgh Sect. A , vol.115 , Issue.1-2 , pp. 167-192
    • Fiedler, B.1    Poláčik, P.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
    • 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 1 (1996) 239-281
    • (1996) J. Differential Equations , vol.125 , Issue.1 , pp. 239-281
    • Fiedler, B.1    Rocha, C.2
  • 71
    • 84971896339 scopus 로고
    • Dynamics of periodically forced parabolic equations on the circle
    • Fiedler B., and Sandstede B. Dynamics of periodically forced parabolic equations on the circle. Ergodic Theory Dynamical Systems 12 3 (1992) 559-571
    • (1992) Ergodic Theory Dynamical Systems , vol.12 , Issue.3 , pp. 559-571
    • Fiedler, B.1    Sandstede, B.2
  • 73
    • 0042237449 scopus 로고    scopus 로고
    • Global solutions of a semilinear parabolic equation
    • Fila M., and Poláčik P. Global solutions of a semilinear parabolic equation. Adv. Differential Equations 4 (1999) 163-196
    • (1999) Adv. Differential Equations , vol.4 , pp. 163-196
    • Fila, M.1    Poláčik, P.2
  • 74
    • 0000095017 scopus 로고
    • Bifurcation and stability of stationary solutions of nonlocal scalar reaction diffusion equations
    • Freitas P. Bifurcation and stability of stationary solutions of nonlocal scalar reaction diffusion equations. J. Dynamics Differential Equations 6 (1994) 613-630
    • (1994) J. Dynamics Differential Equations , vol.6 , pp. 613-630
    • Freitas, P.1
  • 77
    • 0001838115 scopus 로고
    • Transversality between invariant manifolds of periodic orbits for a class of monotone dynamical systems
    • Fusco G., and Oliva W.M. Transversality between invariant manifolds of periodic orbits for a class of monotone dynamical systems. J. Dynamics Differential Equations 2 1 (1990) 1-17
    • (1990) J. Dynamics Differential Equations , vol.2 , Issue.1 , pp. 1-17
    • Fusco, G.1    Oliva, W.M.2
  • 78
    • 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 1 (1991) 111-137
    • (1991) J. Differential Equations , vol.91 , Issue.1 , pp. 111-137
    • Fusco, G.1    Rocha, C.2
  • 80
    • 0031541195 scopus 로고    scopus 로고
    • Continuation of blow-up solutions of nonlinear heat equations in several space dimensions
    • Galaktionov V., and Vázquez J.L. Continuation of blow-up solutions of nonlinear heat equations in several space dimensions. Comm. Pure Appl. Math. 50 (1997) 1-67
    • (1997) Comm. Pure Appl. Math. , vol.50 , pp. 1-67
    • Galaktionov, V.1    Vázquez, J.L.2
  • 81
    • 34250271532 scopus 로고
    • Symmetry and related properties via the maximum principle
    • Gidas B., Ni W.M., and Nirenberg L. Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68 3 (1979) 209-243
    • (1979) Comm. Math. Phys. , vol.68 , Issue.3 , pp. 209-243
    • Gidas, B.1    Ni, W.M.2    Nirenberg, L.3
  • 84
    • 84974185478 scopus 로고
    • Flows on centre manifolds for scalar functional differential equations
    • Hale J.K. Flows on centre manifolds for scalar functional differential equations. Proc. Roy. Soc. Edinburgh Sect. A 101 (1985) 193-201
    • (1985) Proc. Roy. Soc. Edinburgh Sect. A , vol.101 , pp. 193-201
    • Hale, J.K.1
  • 85
    • 0009236644 scopus 로고
    • Local flows for functional differential equations
    • Hale J.K. Local flows for functional differential equations. Contemp. Math. 56 (1986) 185-192
    • (1986) Contemp. Math. , vol.56 , pp. 185-192
    • Hale, J.K.1
  • 87
    • 0011726534 scopus 로고    scopus 로고
    • Dynamics of a scalar parabolic equation
    • Hale J.K. Dynamics of a scalar parabolic equation. Canad. Appl. Math. Quart. 5 3 (1997) 209-305
    • (1997) Canad. Appl. Math. Quart. , vol.5 , Issue.3 , pp. 209-305
    • Hale, J.K.1
  • 88
    • 0040156406 scopus 로고
    • Asymptotic behavior in gradient-like systems
    • Bednarek A.R., and Cesari L. (Eds), Academic Press, New York
    • Hale J.K., and Massatt P. Asymptotic behavior in gradient-like systems. In: Bednarek A.R., and Cesari L. (Eds). Dynamical Systems II (1982), Academic Press, New York 85-101
    • (1982) Dynamical Systems II , pp. 85-101
    • Hale, J.K.1    Massatt, P.2
  • 89
    • 0002555899 scopus 로고
    • Convergence in gradient-like systems with applications to PDE
    • Hale J.K., and Raugel G. Convergence in gradient-like systems with applications to PDE. J. Appl. Math. Phys. (ZAMP) 43 (1992) 63-124
    • (1992) J. Appl. Math. Phys. (ZAMP) , vol.43 , pp. 63-124
    • Hale, J.K.1    Raugel, G.2
  • 90
    • 0002081870 scopus 로고
    • Reaction-diffusion equations on thin domains
    • Hale J.K., and Raugel G. Reaction-diffusion equations 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
  • 91
    • 0039118154 scopus 로고
    • Attractors and Convergence of PDE on Thin L-Shaped Domains
    • Progress in Partial Differential Equations, Longman, Harlow
    • Hale J.K., and Raugel G. Attractors and Convergence of PDE on Thin L-Shaped Domains. Progress in Partial Differential Equations. The Metz Surveys Vol. 2 (1993), Longman, Harlow
    • (1993) The Metz Surveys , vol.2
    • Hale, J.K.1    Raugel, G.2
  • 92
    • 0000746952 scopus 로고    scopus 로고
    • Convergence of solutions of second-order gradient-like systems with analytic nonlinearities
    • Haraux A., and Jendoubi M.A. Convergence of solutions of second-order gradient-like systems with analytic nonlinearities. J. Differential Equations 144 2 (1998) 313-320
    • (1998) J. Differential Equations , vol.144 , Issue.2 , pp. 313-320
    • Haraux, A.1    Jendoubi, M.A.2
  • 93
    • 0000617168 scopus 로고
    • Convergence to a positive equilibrium for some nonlinear evolution equations in a ball
    • Haraux A., and Poláčik P. Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Acta Math. Univ. Comenian. (N.S.) 61 2 (1992) 129-141
    • (1992) Acta Math. Univ. Comenian. (N.S.) , vol.61 , Issue.2 , pp. 129-141
    • Haraux, A.1    Poláčik, P.2
  • 95
    • 46549093257 scopus 로고
    • Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
    • Henry D. Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations. J. Differential Equations 59 (1985) 165-205
    • (1985) J. Differential Equations , vol.59 , pp. 165-205
    • Henry, D.1
  • 96
    • 0000735195 scopus 로고
    • Spatial homogeneity of stable solutions of some periodic-parabolic problems with Neumann boundary conditions
    • Hess P. Spatial homogeneity of stable solutions of some periodic-parabolic problems with Neumann boundary conditions. J. Differential Equations 68 3 (1987) 320-331
    • (1987) J. Differential Equations , vol.68 , Issue.3 , pp. 320-331
    • Hess, P.1
  • 98
    • 21144459956 scopus 로고
    • Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems
    • Hess P., and Poláčik P. Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. SIAM J. Math. Anal. 24 5 (1993) 1312-1330
    • (1993) SIAM J. Math. Anal. , vol.24 , Issue.5 , pp. 1312-1330
    • Hess, P.1    Poláčik, P.2
  • 99
    • 44649169853 scopus 로고
    • Symmetry and convergence properties for non-negative solutions of nonautonomous reaction-diffusion problems
    • Hess P., and Poláčik P. Symmetry and convergence properties for non-negative solutions of nonautonomous reaction-diffusion problems. Proc. Roy. Soc. Edinburgh Sect. A 124 3 (1994) 573-587
    • (1994) Proc. Roy. Soc. Edinburgh Sect. A , vol.124 , Issue.3 , pp. 573-587
    • Hess, P.1    Poláčik, P.2
  • 100
    • 0042171088 scopus 로고
    • Differential equations and convergence almost everywhere in strongly monotone semiflows
    • Amer. Math. Soc., Providence, RI
    • Hirsch M.W. Differential equations and convergence almost everywhere in strongly monotone semiflows. Nonlinear Partial Differential Equations (Durham, NH, 1982) (1983), Amer. Math. Soc., Providence, RI 267-285
    • (1983) Nonlinear Partial Differential Equations (Durham, NH, 1982) , pp. 267-285
    • Hirsch, M.W.1
  • 101
    • 84968480336 scopus 로고
    • The dynamical systems approach to differential equations
    • Hirsch M.W. The dynamical systems approach to differential equations. Bull. Amer. Math. Soc. (N.S.) 11 1 (1984) 1-64
    • (1984) Bull. Amer. Math. Soc. (N.S.) , vol.11 , Issue.1 , pp. 1-64
    • Hirsch, M.W.1
  • 102
    • 33745815315 scopus 로고
    • Stability and convergence in strongly monotone dynamical systems
    • Hirsch M.W. Stability and convergence in strongly monotone dynamical systems. J. Reine Angew. Math. 383 (1988) 1-53
    • (1988) J. Reine Angew. Math. , vol.383 , pp. 1-53
    • Hirsch, M.W.1
  • 105
    • 33646990011 scopus 로고
    • Chain recurrence, semiflows, and gradients
    • Hurley M. Chain recurrence, semiflows, and gradients. J. Dynamics Differential Equations 7 3 (1995) 437-456
    • (1995) J. Dynamics Differential Equations , vol.7 , Issue.3 , pp. 437-456
    • Hurley, M.1
  • 106
    • 0000898687 scopus 로고    scopus 로고
    • Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity
    • Jendoubi M.A. Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity. J. Differential Equations 144 (1998) 302-312
    • (1998) J. Differential Equations , vol.144 , pp. 302-312
    • Jendoubi, M.A.1
  • 107
    • 0000937492 scopus 로고
    • Attractors for strongly monotone flows
    • Jiang J.-F. Attractors for strongly monotone flows. J. Math. Anal. Appl. 162 (1991) 210-222
    • (1991) J. Math. Anal. Appl. , vol.162 , pp. 210-222
    • Jiang, J.-F.1
  • 108
    • 0030586578 scopus 로고    scopus 로고
    • Stable cycles for attractors of strongly monotone discrete-time dynamical systems
    • Jiang J.-F., and Yu S.-X. Stable cycles for attractors of strongly monotone discrete-time dynamical systems. J. Math. Anal. Appl. 202 (1996) 349-362
    • (1996) J. Math. Anal. Appl. , vol.202 , pp. 349-362
    • Jiang, J.-F.1    Yu, S.-X.2
  • 109
    • 0000171235 scopus 로고
    • Explicit construction of an inertial manifold for a reaction diffusion equation
    • Jolly M.S. 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.S.1
  • 111
    • 0002197108 scopus 로고    scopus 로고
    • Symmetry or not?
    • Kawohl B. Symmetry or not?. Math. Intelligencer 20 2 (1998) 16-22
    • (1998) Math. Intelligencer , vol.20 , Issue.2 , pp. 16-22
    • Kawohl, B.1
  • 112
    • 0039575454 scopus 로고    scopus 로고
    • Finite dimensional aspects of semilinear parabolic equations
    • Koch H. Finite dimensional aspects of semilinear parabolic equations. J. Dynamics Differential Equations 8 (1996) 177-202
    • (1996) J. Dynamics Differential Equations , vol.8 , pp. 177-202
    • Koch, H.1
  • 114
    • 0002945715 scopus 로고
    • Linear operators having invariant cone in a Banach space
    • Amer. Math. Soc. Transi., Vol. 26
    • Amer. Math. Soc. Transi., Vol. 26. Krein M.G., and Rutman M.A. Linear operators having invariant cone in a Banach space. Uspekhi Mat. Nauk 3 (1950) 3-95
    • (1950) Uspekhi Mat. Nauk , vol.3 , pp. 3-95
    • Krein, M.G.1    Rutman, M.A.2
  • 115
  • 116
    • 0009344276 scopus 로고
    • Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on bounded domains
    • Li C. Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on bounded domains. Comm. Partial Differential Equations 16 2-3 (1991) 491-526
    • (1991) Comm. Partial Differential Equations , vol.16 , Issue.2-3 , pp. 491-526
    • Li, C.1
  • 117
    • 0001132553 scopus 로고
    • Structure of the set of steady-state solutions and asymptotic behaviour of semilinear heat equations
    • Lions P.L. Structure of the set of steady-state solutions and asymptotic behaviour of semilinear heat equations. J. Differential Equations 53 (1984) 362-386
    • (1984) J. Differential Equations , vol.53 , pp. 362-386
    • Lions, P.L.1
  • 118
    • 0006345676 scopus 로고    scopus 로고
    • Radial and nonradial minimizers for some radially symmetric functionals
    • (electronic, approx. 14 pp.)
    • (electronic, approx. 14 pp.). Lopes O. Radial and nonradial minimizers for some radially symmetric functionals. Electron. J. Differential Equations No. 03 (1996)
    • (1996) Electron. J. Differential Equations , Issue.3
    • Lopes, O.1
  • 119
    • 0001389619 scopus 로고    scopus 로고
    • Radial symmetry of minimizers for some translation and rotation invariant functional
    • Lopes O. Radial symmetry of minimizers for some translation and rotation invariant functional. J. Differential Equations 124 2 (1996) 378-388
    • (1996) J. Differential Equations , vol.124 , Issue.2 , pp. 378-388
    • Lopes, O.1
  • 121
    • 0011023807 scopus 로고
    • Structural stability for scalar parabolic equations
    • Lu K. Structural stability for scalar parabolic equations. J. Differential Equations 114 1 (1994) 253-271
    • (1994) J. Differential Equations , vol.114 , Issue.1 , pp. 253-271
    • Lu, K.1
  • 123
    • 0030102885 scopus 로고    scopus 로고
    • The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
    • Mallet-Paret J., and Sell G.R. The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay. J. Differential Equations 125 2 (1996) 441-489
    • (1996) J. Differential Equations , vol.125 , Issue.2 , pp. 441-489
    • Mallet-Paret, J.1    Sell, G.R.2
  • 124
    • 0030102662 scopus 로고    scopus 로고
    • Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions
    • Mallet-Paret J., and Sell G.R. Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions. J. Differential Equations 125 2 (1996) 385-440
    • (1996) J. Differential Equations , vol.125 , Issue.2 , pp. 385-440
    • Mallet-Paret, J.1    Sell, G.R.2
  • 125
    • 0001051330 scopus 로고
    • The Poincaré-Bendixson theorem for monotone cyclic feedback systems
    • Mallet-Paret J., and Smith H.L. The Poincaré-Bendixson theorem for monotone cyclic feedback systems. J. Dynamics Differential Equations 2 4 (1990) 367-421
    • (1990) J. Dynamics Differential Equations , vol.2 , Issue.4 , pp. 367-421
    • Mallet-Paret, J.1    Smith, H.L.2
  • 126
  • 127
    • 0001989035 scopus 로고
    • Reaction-diffusion systems with time delays monotonicity, invariance, comparison and convergence
    • Martin R.H., and Smith H.L. Reaction-diffusion systems with time delays monotonicity, invariance, comparison and convergence. J. Reine Angew. Math. 413 (1991) 1-35
    • (1991) J. Reine Angew. Math. , vol.413 , pp. 1-35
    • Martin, R.H.1    Smith, H.L.2
  • 128
    • 67649377299 scopus 로고    scopus 로고
    • The convergence of solutions of scalar parabolic equations with convection to periodic solutions
    • Preprint
    • P. Massatt, The convergence of solutions of scalar parabolic equations with convection to periodic solutions, Preprint.
    • Massatt, P.1
  • 129
    • 0000675919 scopus 로고
    • Convergence of solutions of one-dimensional semilinear parabolic equations
    • Matano H. Convergence of solutions of one-dimensional semilinear parabolic equations. J. Math. Kyoto Univ. 18 (1978) 221-227
    • (1978) J. Math. Kyoto Univ. , vol.18 , pp. 221-227
    • Matano, H.1
  • 130
    • 85009592686 scopus 로고
    • Asymptotic behavior and stability of solutions of semilinear diffusion equations
    • Matano H. Asymptotic behavior and stability of solutions of semilinear diffusion equations. Publ. Res. Inst. Math. Sci. 15 (1979) 401-458
    • (1979) Publ. Res. Inst. Math. Sci. , vol.15 , pp. 401-458
    • Matano, H.1
  • 131
    • 0000657925 scopus 로고
    • Nonincrease of the lap-number of a solution for a one-dimensional semilinear parabolic equation
    • Matano H. Nonincrease of the lap-number of a solution for a one-dimensional semilinear parabolic equation. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 2 (1982) 401-441
    • (1982) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.29 , Issue.2 , pp. 401-441
    • Matano, H.1
  • 132
    • 0001166664 scopus 로고
    • Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems
    • Matano H. Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 30 3 (1984) 645-673
    • (1984) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.30 , Issue.3 , pp. 645-673
    • Matano, H.1
  • 133
    • 0001741968 scopus 로고
    • Strongly order-preserving local semidynamical systems-theory and applications
    • (Trieste, 1984), Longman, Harlow
    • (Trieste, 1984). Matano H. Strongly order-preserving local semidynamical systems-theory and applications. Semigroups, Theory and Applications Vol. I (1986), Longman, Harlow 178-185
    • (1986) Semigroups, Theory and Applications , vol.I , pp. 178-185
    • Matano, H.1
  • 136
    • 33747385413 scopus 로고    scopus 로고
    • Stability analysis in order-preserving systems in the presence of symmetry
    • Matano H., and Ogiwara T. Stability analysis in order-preserving systems in the presence of symmetry. Proc. Royal Soc. Edinburgh 129 (1999) 395-438
    • (1999) Proc. Royal Soc. Edinburgh , vol.129 , pp. 395-438
    • Matano, H.1    Ogiwara, T.2
  • 137
    • 3042623067 scopus 로고    scopus 로고
    • Monotonicity and convergence in order-preserving systems
    • Matano H., and Ogiwara T. Monotonicity and convergence in order-preserving systems. Discrete Contin. Dynam. Systems 5 (1999) 1-34
    • (1999) Discrete Contin. Dynam. Systems , vol.5 , pp. 1-34
    • Matano, H.1    Ogiwara, T.2
  • 138
    • 43949149944 scopus 로고
    • Essential manifolds for an elliptic problem in infinite strip
    • Mielke A. Essential manifolds for an elliptic problem in infinite strip. J. Differential Equations 110 (1994) 322-355
    • (1994) J. Differential Equations , vol.110 , pp. 322-355
    • Mielke, A.1
  • 140
    • 84968513736 scopus 로고
    • On monotone trajectories
    • Mierczyński J. On monotone trajectories. Proc. Amer. Math. Soc. 113 2 (1991) 537-544
    • (1991) Proc. Amer. Math. Soc. , vol.113 , Issue.2 , pp. 537-544
    • Mierczyński, J.1
  • 141
    • 84972500224 scopus 로고
    • P-arcs in strongly monotone discrete-time dynamical systems
    • Mierczyński J. P-arcs in strongly monotone discrete-time dynamical systems. Differential Integral Equations 7 5-6 (1994) 1473-1494
    • (1994) Differential Integral Equations , vol.7 , Issue.5-6 , pp. 1473-1494
    • Mierczyński, J.1
  • 142
    • 0031128533 scopus 로고    scopus 로고
    • Globally positive solutions of linear parabolic PDEs of second order with Robin boundary conditions
    • Mierczyński J. Globally positive solutions of linear parabolic PDEs of second order with Robin boundary conditions. J. Math. Anal. Appl. 209 1 (1997) 47-59
    • (1997) J. Math. Anal. Appl. , vol.209 , Issue.1 , pp. 47-59
    • Mierczyński, J.1
  • 143
    • 0002264874 scopus 로고    scopus 로고
    • Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions
    • Mierczyński J. Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions. J. Math. Anal. Appl. 226 2 (1998) 326-347
    • (1998) J. Math. Anal. Appl. , vol.226 , Issue.2 , pp. 326-347
    • Mierczyński, J.1
  • 144
    • 22444453004 scopus 로고    scopus 로고
    • On smoothness of carrying simplices
    • Mierczyński J. On smoothness of carrying simplices. Proc. Amer. Math. Soc. 127 2 (1999) 543-551
    • (1999) Proc. Amer. Math. Soc. , vol.127 , Issue.2 , pp. 543-551
    • Mierczyński, J.1
  • 145
    • 0345987169 scopus 로고
    • Group actions on strongly monotone dynamical systems
    • Mierczyński J., and Poláčik P. Group actions on strongly monotone dynamical systems. Math. Ann. 283 1 (1989) 1-11
    • (1989) Math. Ann. , vol.283 , Issue.1 , pp. 1-11
    • Mierczyński, J.1    Poláčik, P.2
  • 148
    • 0000596044 scopus 로고    scopus 로고
    • Convergence to periodic fronts in a class of semilinear parabolic equations
    • Namah G., and Roquejoffre J.-M. Convergence to periodic fronts in a class of semilinear parabolic equations. Nonlinear Differential Equations Appl. 4 4 (1997) 521-536
    • (1997) Nonlinear Differential Equations Appl. , vol.4 , Issue.4 , pp. 521-536
    • Namah, G.1    Roquejoffre, J.-M.2
  • 149
    • 84941507534 scopus 로고
    • Gestaltaussagen über Lösungen parabolische Differentialgleichungen
    • Nickel K. Gestaltaussagen über Lösungen parabolische Differentialgleichungen. J. Reine Angew. Math. 211 (1962) 78-94
    • (1962) J. Reine Angew. Math. , vol.211 , pp. 78-94
    • Nickel, K.1
  • 152
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • Palmer K. Exponential dichotomies and transversal homoclinic points. J. Differential Equations 55 (1984) 225-256
    • (1984) J. Differential Equations , vol.55 , pp. 225-256
    • Palmer, K.1
  • 154
    • 0002553143 scopus 로고
    • Convergence in smooth strongly monotone flows defined by semilinear parabolic equations
    • Poláčik P. Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. J. Differential Equations 79 1 (1989) 89-110
    • (1989) J. Differential Equations , vol.79 , Issue.1 , pp. 89-110
    • Poláčik, P.1
  • 155
    • 0038225098 scopus 로고
    • Domains of attraction of equilibria and monotonicity properties of convergent trajectories in parabolic systems admitting strong comparison principle
    • Poláčik P. Domains of attraction of equilibria and monotonicity properties of convergent trajectories in parabolic systems admitting strong comparison principle. J. Reine Angew. Math. 400 (1989) 32-56
    • (1989) J. Reine Angew. Math. , vol.400 , pp. 32-56
    • Poláčik, P.1
  • 156
    • 67649303999 scopus 로고
    • Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations
    • North-Holland, Amsterdam
    • Poláčik P. Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Qualitative Theory of Differential Equations (Szeged, 1988) (1990), North-Holland, Amsterdam 519-530
    • (1990) Qualitative Theory of Differential Equations (Szeged, 1988) , pp. 519-530
    • Poláčik, P.1
  • 157
    • 84966242028 scopus 로고
    • Imbedding of any vector field in a scalar semilinear parabolic equation
    • Poláčik P. Imbedding of any vector field in a scalar semilinear parabolic equation. Proc. Amer. Math. Soc. 115 4 (1992) 1001-1008
    • (1992) Proc. Amer. Math. Soc. , vol.115 , Issue.4 , pp. 1001-1008
    • Poláčik, P.1
  • 158
    • 0009235834 scopus 로고
    • Realization of the dynamics of ODEs in scalar parabolic PDEs
    • Equadiff 8 (Bratislava, 1993)
    • Equadiff 8 (Bratislava, 1993). Poláčik P. Realization of the dynamics of ODEs in scalar parabolic PDEs. Tatra Mt. Math. Publ. 4 (1994) 179-185
    • (1994) Tatra Mt. Math. Publ. , vol.4 , pp. 179-185
    • Poláčik, P.1
  • 159
    • 0002215286 scopus 로고
    • High-dimensional ω-limit sets and chaos in scalar parabolic equations
    • Poláčik P. High-dimensional ω-limit sets and chaos in scalar parabolic equations. J. Differential Equations 119 1 (1995) 24-53
    • (1995) J. Differential Equations , vol.119 , Issue.1 , pp. 24-53
    • Poláčik, P.1
  • 160
    • 0009033704 scopus 로고    scopus 로고
    • Reaction-diffusion equations and realization of gradient vector fields
    • World Scientific, River Edge, NJ
    • Poláčik P. Reaction-diffusion equations and realization of gradient vector fields. International Conference on Differential Equations (Lisboa, 1995) (1998), World Scientific, River Edge, NJ 197-206
    • (1998) International Conference on Differential Equations (Lisboa, 1995) , pp. 197-206
    • Poláčik, P.1
  • 161
    • 0009235557 scopus 로고
    • Imbedding vector fields in scalar parabolic Dirichlet BVPs
    • Poláčik P., and Rybakowski K. Imbedding vector fields in scalar parabolic Dirichlet BVPs. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 4 (1995) 737-749
    • (1995) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.22 , Issue.4 , pp. 737-749
    • Poláčik, P.1    Rybakowski, K.2
  • 162
    • 16144369367 scopus 로고    scopus 로고
    • Nonconvergent bounded trajectories in semilinear heat equations
    • Poláčik P., and Rybakowski K.P. Nonconvergent bounded trajectories in semilinear heat equations. J. Differential Equations 124 2 (1996) 472-494
    • (1996) J. Differential Equations , vol.124 , Issue.2 , pp. 472-494
    • Poláčik, P.1    Rybakowski, K.P.2
  • 163
    • 21344468661 scopus 로고    scopus 로고
    • Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation
    • Poláčik P., and Šošovicka V. Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Proc. Roy. Soc. Edinburgh Sect. A 126 4 (1996) 867-884
    • (1996) Proc. Roy. Soc. Edinburgh Sect. A , vol.126 , Issue.4 , pp. 867-884
    • Poláčik, P.1    Šošovicka, V.2
  • 164
    • 34249916235 scopus 로고
    • Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems
    • Poláčik P., and Tereščák I. Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Arch. Rational Mech. Anal. 116 4 (1992) 339-360
    • (1992) Arch. Rational Mech. Anal. , vol.116 , Issue.4 , pp. 339-360
    • Poláčik, P.1    Tereščák, I.2
  • 165
    • 34250074344 scopus 로고
    • Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations
    • Poláčik P., and Tereščák I. Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. J. Dynamics Differential Equations 5 2 (1993) 279-303
    • (1993) J. Dynamics Differential Equations , vol.5 , Issue.2 , pp. 279-303
    • Poláčik, P.1    Tereščák, I.2
  • 166
    • 0035915865 scopus 로고    scopus 로고
    • Existence of stable subharmonic solutions for reaction-diffusion equations
    • Poláčik P., and Yanagida E. Existence of stable subharmonic solutions for reaction-diffusion equations. J. Differential Equations 169 (2001) 255-280
    • (2001) J. Differential Equations , vol.169 , pp. 255-280
    • Poláčik, P.1    Yanagida, E.2
  • 167
    • 67649350538 scopus 로고    scopus 로고
    • Complex dynamics in semilinear parabolic equations
    • ISAS, Trieste
    • Prizzi M. Complex dynamics in semilinear parabolic equations. Ph.D. thesis (1997), ISAS, Trieste
    • (1997) Ph.D. thesis
    • Prizzi, M.1
  • 168
    • 33646903979 scopus 로고    scopus 로고
    • Complicated dynamics of parabolic equations with simple gradient dependence
    • Prizzi M., and Rybakowski K.P. Complicated dynamics of parabolic equations with simple gradient dependence. Trans. Amer. Math. Soc. 350 8 (1998) 3119-3130
    • (1998) Trans. Amer. Math. Soc. , vol.350 , Issue.8 , pp. 3119-3130
    • Prizzi, M.1    Rybakowski, K.P.2
  • 169
    • 0002551910 scopus 로고    scopus 로고
    • Inverse problems and chaotic dynamics of parabolic equations on arbitrary spatial domains
    • Prizzi M., and Rybakowski K.P. Inverse problems and chaotic dynamics of parabolic equations on arbitrary spatial domains. J. Differential Equations 142 1 (1998) 17-53
    • (1998) J. Differential Equations , vol.142 , Issue.1 , pp. 17-53
    • Prizzi, M.1    Rybakowski, K.P.2
  • 171
    • 0001278064 scopus 로고
    • Dynamics of partial differential equations on thin domains
    • Springer, Berlin
    • Raugel G. Dynamics of partial differential equations on thin domains. Dynamical Systems (Montecatini Terme, 1994) (1995), Springer, Berlin 208-315
    • (1995) Dynamical Systems (Montecatini Terme, 1994) , pp. 208-315
    • Raugel, G.1
  • 173
    • 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 4 (1991) 575-591
    • (1991) J. Dynamics Differential Equations , vol.3 , Issue.4 , pp. 575-591
    • Rocha, C.1
  • 174
    • 38149147143 scopus 로고
    • Convergence to traveling waves for solutions of a class of semilinear parabolic equations
    • Roquejoffre J.-M. Convergence to traveling waves for solutions of a class of semilinear parabolic equations. J. Differential Equations 108 2 (1994) 262-295
    • (1994) J. Differential Equations , vol.108 , Issue.2 , pp. 262-295
    • Roquejoffre, J.-M.1
  • 175
    • 0000728498 scopus 로고    scopus 로고
    • Eventual monotonicity and convergence to traveling fronts for the solutions of parabolic equations in cylinders
    • Roquejoffre J.-M. Eventual monotonicity and convergence to traveling fronts for the solutions of parabolic equations in cylinders. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 4 (1997) 499-552
    • (1997) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.14 , Issue.4 , pp. 499-552
    • Roquejoffre, J.-M.1
  • 176
    • 0002890056 scopus 로고
    • Analycity properties of the characteristic exponents of random matrix products
    • Ruelle D. Analycity properties of the characteristic exponents of random matrix products. Adv. in Math. 32 1 (1979) 68-80
    • (1979) Adv. in Math. , vol.32 , Issue.1 , pp. 68-80
    • Ruelle, D.1
  • 177
    • 0000466179 scopus 로고
    • An abstract approach to smoothness of invariant manifolds
    • Rybakowski K.P. An abstract approach to smoothness of invariant manifolds. Appl. Anal. 49 1-2 (1993) 119-150
    • (1993) Appl. Anal. , vol.49 , Issue.1-2 , pp. 119-150
    • Rybakowski, K.P.1
  • 178
    • 0009291003 scopus 로고
    • Realization of arbitrary vector fields on center manifolds of parabolic Dirichlet BVPs
    • Rybakowski K.P. Realization of arbitrary vector fields on center manifolds of parabolic Dirichlet BVPs. J. Differential Equations 114 1 (1994) 199-221
    • (1994) J. Differential Equations , vol.114 , Issue.1 , pp. 199-221
    • Rybakowski, K.P.1
  • 179
    • 0001638041 scopus 로고
    • Realization of arbitrary vector fields on invariant manifolds of delay equations
    • Rybakowski K.P. Realization of arbitrary vector fields on invariant manifolds of delay equations. J. Differential Equations 114 1 (1994) 222-231
    • (1994) J. Differential Equations , vol.114 , Issue.1 , pp. 222-231
    • Rybakowski, K.P.1
  • 181
    • 67649346546 scopus 로고
    • Asymptotic behavior of solutions of nonautonomous scalar reaction-diffusion equations
    • 2 (Barcelona, 1991), World Scientific, River Edge, NJ
    • 2 (Barcelona, 1991). Sandstede B. Asymptotic behavior of solutions of nonautonomous scalar reaction-diffusion equations. International Conference on Differential Equations Vols. 1 (1993), World Scientific, River Edge, NJ 888-892
    • (1993) International Conference on Differential Equations , vol.1 , pp. 888-892
    • Sandstede, B.1
  • 182
    • 0001358147 scopus 로고
    • A symmetry problem in potential theory
    • Serrin J. A symmetry problem in potential theory. Arch. Rational Mech. Anal. 43 (1971) 304-318
    • (1971) Arch. Rational Mech. Anal. , vol.43 , pp. 304-318
    • Serrin, J.1
  • 183
    • 0013080113 scopus 로고    scopus 로고
    • Almost automorphic and almost periodic dynamics in skew-product semiflows
    • Shen W., and Yi Y. Almost automorphic and almost periodic dynamics in skew-product semiflows. Mem. Amer. Math. Soc. 647 (1998) 1-93
    • (1998) Mem. Amer. Math. Soc. , vol.647 , pp. 1-93
    • Shen, W.1    Yi, Y.2
  • 184
    • 0000137102 scopus 로고
    • Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems
    • Simon L. Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems. Ann. of Math. 118 (1983) 525-571
    • (1983) Ann. of Math. , vol.118 , pp. 525-571
    • Simon, L.1
  • 185
    • 0038840779 scopus 로고
    • Invariant curves for mappings
    • Smith H.L. Invariant curves for mappings. SIAM J. Math. Anal. 17 5 (1986) 1053-1067
    • (1986) SIAM J. Math. Anal. , vol.17 , Issue.5 , pp. 1053-1067
    • Smith, H.L.1
  • 187
    • 0000168647 scopus 로고
    • Quasi convergence and stability for strongly order-preserving semiflows
    • Smith H.L., and Thieme H.R. Quasi convergence and stability for strongly order-preserving semiflows. SIAM J. Math. Anal. 21 3 (1990) 673-692
    • (1990) SIAM J. Math. Anal. , vol.21 , Issue.3 , pp. 673-692
    • Smith, H.L.1    Thieme, H.R.2
  • 188
    • 0001113507 scopus 로고
    • Convergence for strongly order-preserving semiflows
    • Smith H.L., and Thieme H.R. Convergence for strongly order-preserving semiflows. SIAM J. Math. Anal. 22 4 (1991) 1081-1101
    • (1991) SIAM J. Math. Anal. , vol.22 , Issue.4 , pp. 1081-1101
    • Smith, H.L.1    Thieme, H.R.2
  • 190
    • 0001726711 scopus 로고
    • Symmetry-breaking for positive solutions of semilinear elliptic equations
    • Smoller J., and Wasserman A. Symmetry-breaking for positive solutions of semilinear elliptic equations. Arch. Rat. Mech. Anal. 95 (1986) 217-225
    • (1986) Arch. Rat. Mech. Anal. , vol.95 , pp. 217-225
    • Smoller, J.1    Wasserman, A.2
  • 191
    • 0025425054 scopus 로고
    • Convergence to equilibrium on invariant d-hypersurf ace s for strongly increasing discrete-time semigroups
    • Takáč P. Convergence to equilibrium on invariant d-hypersurf ace s for strongly increasing discrete-time semigroups. J. Math. Anal. Appl. 148 1 (1990) 223-244
    • (1990) J. Math. Anal. Appl. , vol.148 , Issue.1 , pp. 223-244
    • Takáč, P.1
  • 192
    • 38249009294 scopus 로고
    • Asymptotic behavior of strongly monotone time-periodic dynamical processes with symmetry
    • Takáč P. Asymptotic behavior of strongly monotone time-periodic dynamical processes with symmetry. J. Differential Equations 100 2 (1992) 355-378
    • (1992) J. Differential Equations , vol.100 , Issue.2 , pp. 355-378
    • Takáč, P.1
  • 193
    • 4243550804 scopus 로고
    • Domains of attraction of generic ω-limit sets for strongly monotone discrete-time semigroups
    • Takáč P. Domains of attraction of generic ω-limit sets for strongly monotone discrete-time semigroups. J. Reine Angew. Math. 423 (1992) 101-173
    • (1992) J. Reine Angew. Math. , vol.423 , pp. 101-173
    • Takáč, P.1
  • 194
    • 0001043836 scopus 로고
    • Linearly stable subharmonic orbits in strongly monotone time-periodic dynamical systems
    • Takáč P. Linearly stable subharmonic orbits in strongly monotone time-periodic dynamical systems. Proc. Amer. Math. Soc. 115 3 (1992) 691-698
    • (1992) Proc. Amer. Math. Soc. , vol.115 , Issue.3 , pp. 691-698
    • Takáč, P.1
  • 195
    • 0000055435 scopus 로고
    • A construction of stable subharmonic orbits in monotone time-periodic dynamical systems
    • Takáč P. A construction of stable subharmonic orbits in monotone time-periodic dynamical systems. Monatsh. Math. 115 3 (1993) 215-244
    • (1993) Monatsh. Math. , vol.115 , Issue.3 , pp. 215-244
    • Takáč, P.1
  • 196
    • 0011625282 scopus 로고
    • A short elementary proof of the Krein-Rutman theorem
    • Takáč P. A short elementary proof of the Krein-Rutman theorem. Houston J. Math. 20 1 (1994) 93-98
    • (1994) Houston J. Math. , vol.20 , Issue.1 , pp. 93-98
    • Takáč, P.1
  • 197
    • 0003479527 scopus 로고    scopus 로고
    • 1 smooth strongly monotone discrete-time dynamical systems
    • Preprint
    • 1 smooth strongly monotone discrete-time dynamical systems, Preprint.
    • Tereščák, I.1
  • 198
    • 33646880135 scopus 로고
    • Dynamical systems with discrete Lyapunov functionals
    • Comenius University
    • Tereščák I. Dynamical systems with discrete Lyapunov functionals. Ph.D. thesis (1994), Comenius University
    • (1994) Ph.D. thesis
    • Tereščák, I.1
  • 199
    • 0000031198 scopus 로고
    • Symmetry properties in systems of semilinear elliptic equations
    • Troy W.C. Symmetry properties in systems of semilinear elliptic equations. J. Differential Equations 42 3 (1981) 400-413
    • (1981) J. Differential Equations , vol.42 , Issue.3 , pp. 400-413
    • Troy, W.C.1
  • 200
    • 0009227632 scopus 로고
    • Existence of Ruelle-Takens transition to chaos for some evolution equations
    • Vakulenko S.A. Existence of Ruelle-Takens transition to chaos for some evolution equations. C. R. Acad. Sci. Paris 316 (1993) 1015-1018
    • (1993) C. R. Acad. Sci. Paris , vol.316 , pp. 1015-1018
    • Vakulenko, S.A.1
  • 201
    • 0009294782 scopus 로고    scopus 로고
    • Reaction-diffusion systems with prescribed large time behavior
    • Vakulenko S.A. Reaction-diffusion systems with prescribed large time behavior. Ann. Inst. Henri Poincaré 66 (1997) 373-410
    • (1997) Ann. Inst. Henri Poincaré , vol.66 , pp. 373-410
    • Vakulenko, S.A.1
  • 202
    • 67649325547 scopus 로고    scopus 로고
    • Dissipative systems with controllable inertial forms
    • Preprint
    • S.A. Vakulenko, Dissipative systems with controllable inertial forms, Preprint.
    • Vakulenko, S.A.1
  • 203
    • 34250098668 scopus 로고
    • Symmetry-breaking at positive solutions
    • Vanderbauwhede A. Symmetry-breaking at positive solutions. Z. Angew. Math. Phys. 38 2 (1987) 315-326
    • (1987) Z. Angew. Math. Phys. , vol.38 , Issue.2 , pp. 315-326
    • Vanderbauwhede, A.1
  • 204
    • 0002876557 scopus 로고
    • Centre manifolds, normal forms and elementary bifurcations
    • Wiley, Chichester
    • Vanderbauwhede A. Centre manifolds, normal forms and elementary bifurcations. Dynamics Reported Vol. 2 (1989), Wiley, Chichester 89-169
    • (1989) Dynamics Reported , vol.2 , pp. 89-169
    • Vanderbauwhede, A.1
  • 206
    • 0002283608 scopus 로고
    • Stabilization of solutions of weakly coupled cooperative parabolic systems
    • Vishnevskii M.P. Stabilization of solutions of weakly coupled cooperative parabolic systems. Mat. Sb. 183 (1992) 45-62
    • (1992) Mat. Sb. , vol.183 , pp. 45-62
    • Vishnevskii, M.P.1
  • 207
    • 84969589882 scopus 로고
    • Monotone solutions of quasilinear parabolic equations
    • ii, viii
    • ii, viii. Vishnevskii M.P. Monotone solutions of quasilinear parabolic equations. Sibirsk. Mat. Zh. 34 4 (1993) 50-60
    • (1993) Sibirsk. Mat. Zh. , vol.34 , Issue.4 , pp. 50-60
    • Vishnevskii, M.P.1
  • 208
    • 0000565429 scopus 로고
    • n, III: Center curves and Lyapunov stability
    • n, III: Center curves and Lyapunov stability. Nonlinear Anal. 22 5 (1994) 533-559
    • (1994) Nonlinear Anal. , vol.22 , Issue.5 , pp. 533-559
    • Vuillermot, P.1
  • 212
    • 0001883857 scopus 로고
    • Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable
    • Zelenyak T.I. Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable. Differential Equations (transi, from Differencialnye Uravnenia) 4 (1968) 17-22
    • (1968) Differential Equations (transi, from Differencialnye Uravnenia) , vol.4 , pp. 17-22
    • Zelenyak, T.I.1


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