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All issues Volume 23 / No 3 (1989) ESAIM: M2AN, 23 3 (1989) 445-461 References
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ESAIM: M2AN
Volume 23, Number 3, 1989
Attractors, Inertial Manifolds and their Approximation. Proceedings of the Marseille-Luminy... 1987
Page(s) 445 - 461
DOI https://doi.org/10.1051/m2an/1989230304451
Published online 31 January 2017
  1. J. E. BILLOTTI, J. P. LASALLE (1971), Dissipative periodic processes, Bull. Amer.Math. Soc, 77, pp. 1082-1088. [MR: 284682] [Zbl: 0274.34061] [Google Scholar]
  2. S.-N. CHOW, K. LU and G. R. SELL (1988), Smoothness of inertial manifolds, Preprint. [MR: 1180685] [Zbl: 0767.58026] [Google Scholar]
  3. P. CONSTANTIN (1988), A construction of inertial manifolds, Preprint. [MR: 1034492] [Zbl: 0691.58040] [Google Scholar]
  4. P. CONSTANTIN, C. FOIAS, B. NICOLAENKO, R. TEMAM (1989), Integral manifolds and inertial manifolds for dissipative partial differential equations, Applied Mathematical Sciences, No 70, Springer-Verlag. [MR: 966192] [Zbl: 0683.58002] [Google Scholar]
  5. P. CONSTANTIN, C. FOIAS, B. NICOLAENKO, R. TEMAM (1989), Spectral barriers and inertial manifolds for dissipative partial differential equations, J Dynamics and Differential Equations, 1 (to appear). [MR: 1010960] [Zbl: 0701.35024] [Google Scholar]
  6. P. CONSTANTIN, C. FOIAS, R. TEMAM (1985), Attractors representing turbulent flows, Memoirs Amer. Math. Soc., 314. [MR: 776345] [Zbl: 0567.35070] [Google Scholar]
  7. C. R. DOERING, J. D. GIBBON, D. D. HOLM and B. NICOLAENKO (1988), Low dimensional behavior in the complex Ginzburg-Landau equation, Nonlinearity (to appear). [MR: 937004] [Zbl: 0655.58021] [Google Scholar]
  8. E. FABES, M. LUSKIN and G. R. SELL (1988), Construction of inertial manifolds by elliptic regularization, J. Differential Equations, to appear. [MR: 1091482] [Zbl: 0728.34047] [Google Scholar]
  9. C. FOIAS, M. S. JOLLY, I. G. KEVREKIDIS, G. R. SELL, E. S. TITI (1988), On the computation of inertial manifolds, Physics Letters A, Vol. 131, No 7, 8, pp. 433-436. [MR: 972615] [Google Scholar]
  10. C. FOIAS, B. NICOLAENKO, G. R. SELL, R. TEMAM (1988), Inertial manifolds for the Kuramoto Sivashinsky equation and an estimate of their lowest dimensions, J. Math. Pures Appl., 67, pp. 197-226. [MR: 964170] [Zbl: 0694.35028] [Google Scholar]
  11. C. FOIAS, G. R. SELL and R. TEMAM (1986), Inertial manifolds for nonlinear evolutionary equations, IMA Preprint No 234, March, 1986 Also in, J. Differential Equations, 73 (1988), pp. 309-353. [MR: 943945] [Zbl: 0643.58004] [Google Scholar]
  12. C. FOIAS, G. R. SELL and E. S. TITI (1988), Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations, J. Dynamics and Differential Equations, to appear. [MR: 1010966] [Zbl: 0692.35053] [Google Scholar]
  13. C. FOIAS and R. TEMAM (1979), Some analytic and geometric properties of the solutions of the Navier-Stokes equations, J. Math. Pures Appl., 58, pp. 339-368. [MR: 544257] [Zbl: 0454.35073] [Google Scholar]
  14. J.-M. GHIDAGLIA, Discrétisation en temps et variétés inertielles pour des équations d'évolution aux dérivées partielles non linéaires, Preprint. [Zbl: 0666.35049] [Google Scholar]
  15. J. K. HALE (1988), Asymptotic Behavior of Dissipative Systems, Amer. Math. Soc., Providence. [MR: 941371] [Zbl: 0642.58013] [Google Scholar]
  16. J. K. HALE and G. R. SELL (1988), Inertial manifolds for gradient Systems. [Google Scholar]
  17. D. HENRY (1981), Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, No 840, Springer-Verlag, New York. [MR: 610244] [Zbl: 0456.35001] [Google Scholar]
  18. M. S. JOLLY (1988), Explicit construction of an inertial manifold for a reaction diffusion equation, J. Differential Equations (to appear). [MR: 992147] [Zbl: 0691.35049] [Google Scholar]
  19. D. A. KAMAEV (1981), Hopf's conjecture for a class of chemical kinetics equations, J. Soviet Math., 25, pp. 836-849. [Zbl: 0531.35040] [Google Scholar]
  20. M. LUSKIN and G. R. SELL (1988), Parabolic regularization and the construction of inertial manifolds, Preprint. [Google Scholar]
  21. J. MALLET-PARET (1976), Negatively invariant sets of compact maps and an extension of a theorem of Cartwright, J. Differential Equations, 22, pp. 331-348. [MR: 423399] [Zbl: 0354.34072] [Google Scholar]
  22. J. MALLET-PARET and G. R. SELL (1987), Inertial manifolds for reaction diffusion equations in higher space dimensions, IMA Preprint No. 331, June 1987, Also in, J. Amer. Math. Soc, 1, No. 4 (1988), pp. 805-866. [MR: 943276] [Zbl: 0674.35049] [Google Scholar]
  23. R. MANÉ (1977), Reduction of semilinear parabolic equations to finite dimensional C1 flows, Geometry and Topology, Lecture Notes in Math., vol. 597, Springer-Verlag, New York, pp.361-378. [MR: 451309] [Zbl: 0412.35049] [Google Scholar]
  24. R. MANÉ, (1981) On the dimension of the compact invariant sets of certain nonlinear maps, Lecture Notes in Math, vol. 898, Springer-Verlag, New York, pp. 230-242. [MR: 654892] [Zbl: 0544.58014] [Google Scholar]
  25. M. MARION (1988), Inertial manifolds associated to partly dissipative reaction diffusion equations, J. Math. Anal. Appl. (to appear). [Zbl: 0689.58039] [Google Scholar]
  26. X. MORA (1983), Finite dimensional attracting manifolds in reaction diffusion equations, Contemporary Math., 17, pp. 353-360. [MR: 706109] [Zbl: 0525.35046] [Google Scholar]
  27. X. MORA and J. SOLÀ-MORALES (1987), Existence and non-existence of finite dimensional globally attracting invariant manifolds in semilinear damped wave equations, Dynamics of Infinite Dimensional Systems, Springer-Verlag, New York, pp. 187-210. [MR: 921912] [Zbl: 0642.35062] [Google Scholar]
  28. X. MORA and J. SOLÀ-MORALES (1988), The singular limit dynamics of semilinear damped wave equations, Preprint, Univ. Autònoma Barcelona. [MR: 992148] [Zbl: 0699.35177] [Google Scholar]
  29. B. NICOLAENKO, B. SCHEURER and R. TEMAM, (1987), Some global dynamical properties of a class of pattern formation equations, IMA Preprint No. 381. [MR: 976973] [Zbl: 0691.35019] [Google Scholar]
  30. A. PAZY (1983), Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, Vol.44, Springer-Verlag, New York. [MR: 710486] [Zbl: 0516.47023] [Google Scholar]
  31. R. J. SACKER (1964), On invariant surfaces and bifurcation of periodic solutions of ordinary differential equations, NYU Preprint No. 333, October 1964. [Google Scholar]
  32. R. J. SACKER (1965), A new approach to the perturbation theory of invariant surfaces, Comm. Pure Appl. Math., 18, pp.717-732. [MR: 188566] [Zbl: 0133.35501] [Google Scholar]
  33. R. J. SACKER (1969), A perturbation theorem for invariant manifolds and Hölder continuity, J. Math. Mech., 18, pp.705-762. [MR: 239221] [Zbl: 0218.34046] [Google Scholar]
  34. G. R. SELL and Y. YOU (1988), Inertial manifolds : The non self adjoint case, Preprint. [Zbl: 0760.34051] [Google Scholar]
  35. M. TABOADA (1988), Finite dimensional asymptotic behavior for the Swift-Hohenberg model of convection, Nonlinear Analysis, TMA, to appear. [MR: 1028246] [Zbl: 0707.58019] [Google Scholar]
  36. R. TEMAM (1988), Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York. [MR: 953967] [Zbl: 0662.35001] [Google Scholar]

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