메뉴 건너뛰기




Volumn 219, Issue 2, 1998, Pages 479-502

Persistence of Invariant Sets for Dissipative Evolution Equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0010599996     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5847     Document Type: Article
Times cited : (18)

References (39)
  • 1
    • 0000404607 scopus 로고
    • On the qualitative behavior of the orbits of a parabolic partial differential equations and its discretization in the neighborhood of a hyperbolic fixed point
    • Alouges F., Debussche A. On the qualitative behavior of the orbits of a parabolic partial differential equations and its discretization in the neighborhood of a hyperbolic fixed point. Numer. Funct. Anal. Optim. 12:1991;253-269.
    • (1991) Numer. Funct. Anal. Optim. , vol.12 , pp. 253-269
    • Alouges, F.1    Debussche, A.2
  • 3
    • 0001500810 scopus 로고
    • On invariant closed curves for one-step methods
    • Beyn W.-J. On invariant closed curves for one-step methods. Numer. Math. 51:1987;103-122.
    • (1987) Numer. Math. , vol.51 , pp. 103-122
    • Beyn, W.-J.1
  • 4
    • 0007108344 scopus 로고
    • Center manifolds of dynamical systems under discretization
    • Beyn W.-J., Lorenz J. Center manifolds of dynamical systems under discretization. Numer. Funct. Anal. Optim. 9:1987;381-414.
    • (1987) Numer. Funct. Anal. Optim. , vol.9 , pp. 381-414
    • Beyn, W.-J.1    Lorenz, J.2
  • 6
    • 0003368378 scopus 로고
    • Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations
    • New York/Berlin: Springer-Verlag
    • Constantin P., Foias C., Nicolaenko B., Temam R. Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations. Applied Mathematics Sciences. 70:1988;Springer-Verlag, New York/Berlin.
    • (1988) Applied Mathematics Sciences , vol.70
    • Constantin, P.1    Foias, C.2    Nicolaenko, B.3    Temam, R.4
  • 8
    • 0021480034 scopus 로고
    • On the large time Galerkin approximation of the Navier-Stokes equations
    • Constantin P., Foias C., Temam R. On the large time Galerkin approximation of the Navier-Stokes equations. SIAM J. Numer. Anal. 21:1984;615-634.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 615-634
    • Constantin, P.1    Foias, C.2    Temam, R.3
  • 9
    • 0011541653 scopus 로고
    • Some remarks on the smoothness of inertial manifolds
    • Demengel F., Ghidaglia J.-M. Some remarks on the smoothness of inertial manifolds. Nonlinear Anal. 16:1991;79-87.
    • (1991) Nonlinear Anal. , vol.16 , pp. 79-87
    • Demengel, F.1    Ghidaglia, J.-M.2
  • 11
    • 0000766179 scopus 로고
    • Construction of inertial manifolds by elliptic regularization
    • Fabes E., Luskin M., Sell G. Construction of inertial manifolds by elliptic regularization. J. Differential Equations. 89:1991;355-387.
    • (1991) J. Differential Equations , vol.89 , pp. 355-387
    • Fabes, E.1    Luskin, M.2    Sell, G.3
  • 12
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • Fenichel N. Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21:1971;193-226.
    • (1971) Indiana Univ. Math. J. , vol.21 , pp. 193-226
    • Fenichel, N.1
  • 13
    • 0001047390 scopus 로고
    • Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimensions
    • Foias C., Nicolaenko B., Sell G. R., Temam R. Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimensions. J. Math. Pures Appl. 67:1988b;197-226.
    • (1988) J. Math. Pures Appl. , vol.67 , pp. 197-226
    • Foias, C.1    Nicolaenko, B.2    Sell, G.R.3    Temam, R.4
  • 14
    • 0000076092 scopus 로고
    • Variétés inertielles deséquations différentielles dissipatives
    • Foias C., Sell G., Temam R. Variétés inertielles deséquations différentielles dissipatives. C. R. Acad. Sci. Paris Sér. I. 301:1985;139-142.
    • (1985) C. R. Acad. Sci. Paris Sér. I , vol.301 , pp. 139-142
    • Foias, C.1    Sell, G.2    Temam, R.3
  • 15
    • 0000640733 scopus 로고
    • Inertial manifolds for nonlinear evolutionary equations
    • Foias C., Sell G., 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
  • 16
    • 0001686992 scopus 로고
    • Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
    • Foias C., Sell G., Titi E. S. Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations. J. Dynamics and Differential Equations. 1:1989;199-243.
    • (1989) J. Dynamics and Differential Equations , vol.1 , pp. 199-243
    • Foias, C.1    Sell, G.2    Titi, E.S.3
  • 17
    • 0000166593 scopus 로고
    • Determining nodes, finite difference schemes and inertial manifolds
    • Foias C., Titi E. S. Determining nodes, finite difference schemes and inertial manifolds. Nonlinearity. 4:1991;135-153.
    • (1991) Nonlinearity , vol.4 , pp. 135-153
    • Foias, C.1    Titi, E.S.2
  • 18
    • 0003293929 scopus 로고
    • Asymptotic Behavior of Dissipative Systems
    • Providence: Amer. Math. Soc.
    • Hale J. K. Asymptotic Behavior of Dissipative Systems. Mathematical Surveys and Monographs. 25:1988;Amer. Math. Soc. Providence.
    • (1988) Mathematical Surveys and Monographs , vol.25
    • Hale, J.K.1
  • 19
    • 0003460899 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • New York: Springer-Verlag
    • Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics. 1981;Springer-Verlag, New York.
    • (1981) Lecture Notes in Mathematics
    • Henry, D.1
  • 20
    • 0040738943 scopus 로고
    • Finite element approximation of the nonstationary Navier-Stokes problems. Part II Stability of solutions and error estimates uniform in time
    • Heywood J. G., Rannacher R. Finite element approximation of the nonstationary Navier-Stokes problems. Part II Stability of solutions and error estimates uniform in time. SIAM J. Numer. Anal. 21:1986;615-634.
    • (1986) SIAM J. Numer. Anal. , vol.21 , pp. 615-634
    • Heywood, J.G.1    Rannacher, R.2
  • 22
    • 0011601917 scopus 로고
    • On the behavior of attractors under finite difference approximation
    • Jones D. A. On the behavior of attractors under finite difference approximation. Numer. Funct. Anal. Optim. 16:1995;1155-1180.
    • (1995) Numer. Funct. Anal. Optim. , vol.16 , pp. 1155-1180
    • Jones, D.A.1
  • 23
    • 85045781318 scopus 로고    scopus 로고
    • Perisitence of invariant manifolds for nonlinear PDEs
    • D. A. Jones, S. Shkoller, Perisitence of invariant manifolds for nonlinear PDEs, Stud. Appl. Math.
    • Stud. Appl. Math.
    • Jones, D.A.1    Shkoller, S.2
  • 24
    • 0000868591 scopus 로고
    • Attractive invariant manifolds under approximation: Inertial manifolds
    • Jones D. A., Stuart A. M. Attractive invariant manifolds under approximation: Inertial manifolds. J. Differential Equations. 123:1995;588-637.
    • (1995) J. Differential Equations , vol.123 , pp. 588-637
    • Jones, D.A.1    Stuart, A.M.2
  • 26
    • 0000649975 scopus 로고
    • Stable attracting sets in dynamical systems and their one-step discretizations
    • Kloeden P., Lorenz J. Stable attracting sets in dynamical systems and their one-step discretizations. SIAM J. Numer. Anal. 23:1986;986-995.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 986-995
    • Kloeden, P.1    Lorenz, J.2
  • 27
    • 0028484839 scopus 로고
    • The behaviour of finite element solutions of semi-linear parabolic problems near stationary points
    • Larsson S., Sanz-Serna J. M. The behaviour of finite element solutions of semi-linear parabolic problems near stationary points. SIAM J. Numer. Anal. 31:1994;1000-1018.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1000-1018
    • Larsson, S.1    Sanz-Serna, J.M.2
  • 29
    • 0009228949 scopus 로고    scopus 로고
    • Attractors and inertial manifolds for finite difference approximations of the complex Ginzburg-Landau equation
    • G. J. Lord, Attractors and inertial manifolds for finite difference approximations of the complex Ginzburg-Landau equation, SIAM J. Numer. Anal.
    • SIAM J. Numer. Anal.
    • Lord, G.J.1
  • 30
    • 84968508885 scopus 로고
    • Inertial manifolds for reaction diffusion equations in higher space dimensions
    • Mallet-Paret J., Sell G. Inertial manifolds for reaction diffusion equations in higher space dimensions. 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
  • 31
    • 0011536003 scopus 로고
    • Analysis of regularized Navier-Stokes equations, II
    • Ou Y.-R., Sritharan S. S. Analysis of regularized Navier-Stokes equations, II. Quart. Appl. Math. 49:1991;687-728.
    • (1991) Quart. Appl. Math. , vol.49 , pp. 687-728
    • Ou, Y.-R.1    Sritharan, S.S.2
  • 33
    • 0002883676 scopus 로고
    • Perturbations of attractors of differential equations
    • Pliss V. A., Sell G. R. Perturbations of attractors of differential equations. J. Differential Equations. 92:1991;100-124.
    • (1991) J. Differential Equations , vol.92 , pp. 100-124
    • Pliss, V.A.1    Sell, G.R.2
  • 34
    • 0001065397 scopus 로고
    • A perturbation theorem for invariant manifolds and Hölder continuity
    • Sacker R. J. A perturbation theorem for invariant manifolds and Hölder continuity. J. Math. Mech. 18:1969;705-762.
    • (1969) J. Math. Mech. , vol.18 , pp. 705-762
    • Sacker, R.J.1
  • 35
    • 38249012311 scopus 로고
    • Inertial manifolds: The non-self-adjoint case
    • Sell G. R., You Y. Inertial manifolds: The non-self-adjoint case. J. Differential Equations. 96:1992;203-255.
    • (1992) J. Differential Equations , vol.96 , pp. 203-255
    • Sell, G.R.1    You, Y.2
  • 36
    • 0000441660 scopus 로고
    • Perturbation theory for infinite-dimensional dynamical systems
    • M. Ainsworth, J. Levesley, W.A. Light, & M. Marletta.
    • Stuart A. M. Perturbation theory for infinite-dimensional dynamical systems. Ainsworth M., Levesley J., Light W. A., Marletta M. Theory and Numerics of Ordinary and Partial Differential Equations. 1994.
    • (1994) Theory and Numerics of Ordinary and Partial Differential Equations
    • Stuart, A.M.1
  • 38
    • 0023420776 scopus 로고
    • On a criterion for locating stable stationary solutions to the Navier-Stokes equations
    • Titi E. S. On a criterion for locating stable stationary solutions to the Navier-Stokes equations. Nonlinear Anal. 11:1987;1085-1102.
    • (1987) Nonlinear Anal. , vol.11 , pp. 1085-1102
    • Titi, E.S.1
  • 39
    • 0011538645 scopus 로고
    • Un critère pour l'approximation des solutions périodiques des équations de Navier-Stokes
    • Titi E. S. Un critère pour l'approximation des solutions périodiques des équations de Navier-Stokes. C.R. Acad. Sci. Paris Sér. I. 312:1991;41-43.
    • (1991) C.R. Acad. Sci. Paris Sér. I , vol.312 , pp. 41-43
    • Titi, E.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.