Approximation theories for inertial manifolds

 Access to full text

 Full (PDF)

1. J. E. BILLOTTI, J. P. LASALLE (1971), Dissipative periodic processes, Bull. Amer.Math. Soc, 77, pp. 1082-1088. Zbl0274.34061MR284682
2. S.-N. CHOW, K. LU and G. R. SELL (1988), Smoothness of inertial manifolds, Preprint. Zbl0767.58026MR1180685
3. P. CONSTANTIN (1988), A construction of inertial manifolds, Preprint. Zbl0691.58040MR1034492
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. Zbl0683.58002MR966192
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). Zbl0701.35024MR1010960
6. P. CONSTANTIN, C. FOIAS, R. TEMAM (1985), Attractors representing turbulent flows, Memoirs Amer. Math. Soc., 314. Zbl0567.35070MR776345
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). Zbl0655.58021MR937004
8. E. FABES, M. LUSKIN and G. R. SELL (1988), Construction of inertial manifolds by elliptic regularization, J. Differential Equations, to appear. Zbl0728.34047MR1091482
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. MR972615
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. Zbl0694.35028MR964170
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. Zbl0643.58004MR943945
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. Zbl0692.35053MR1010966
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. Zbl0454.35073MR544257
14. J.-M. GHIDAGLIA, Discrétisation en temps et variétés inertielles pour des équations d'évolution aux dérivées partielles non linéaires, Preprint. Zbl0666.35049
15. J. K. HALE (1988), Asymptotic Behavior of Dissipative Systems, Amer. Math. Soc., Providence. Zbl0642.58013MR941371
16. J. K. HALE and G. R. SELL (1988), Inertial manifolds for gradient Systems. 
17. D. HENRY (1981), Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, No 840, Springer-Verlag, New York. Zbl0456.35001MR610244
18. M. S. JOLLY (1988), Explicit construction of an inertial manifold for a reaction diffusion equation, J. Differential Equations (to appear). Zbl0691.35049MR992147
19. D. A. KAMAEV (1981), Hopf's conjecture for a class of chemical kinetics equations, J. Soviet Math., 25, pp. 836-849. Zbl0531.35040
20. M. LUSKIN and G. R. SELL (1988), Parabolic regularization and the construction of inertial manifolds, Preprint. 
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. Zbl0354.34072MR423399
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. Zbl0674.35049MR943276
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. Zbl0412.35049MR451309
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. Zbl0544.58014MR654892
25. M. MARION (1988), Inertial manifolds associated to partly dissipative reaction diffusion equations, J. Math. Anal. Appl. (to appear). Zbl0689.58039
26. X. MORA (1983), Finite dimensional attracting manifolds in reaction diffusion equations, Contemporary Math., 17, pp. 353-360. Zbl0525.35046MR706109
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. Zbl0642.35062MR921912
28. X. MORA and J. SOLÀ-MORALES (1988), The singular limit dynamics of semilinear damped wave equations, Preprint, Univ. Autònoma Barcelona. Zbl0699.35177MR992148
29. B. NICOLAENKO, B. SCHEURER and R. TEMAM, (1987), Some global dynamical properties of a class of pattern formation equations, IMA Preprint No. 381. Zbl0691.35019MR976973
30. A. PAZY (1983), Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, Vol.44, Springer-Verlag, New York. Zbl0516.47023MR710486
31. R. J. SACKER (1964), On invariant surfaces and bifurcation of periodic solutions of ordinary differential equations, NYU Preprint No. 333, October 1964. 
32. R. J. SACKER (1965), A new approach to the perturbation theory of invariant surfaces, Comm. Pure Appl. Math., 18, pp.717-732. Zbl0133.35501MR188566
33. R. J. SACKER (1969), A perturbation theorem for invariant manifolds and Hölder continuity, J. Math. Mech., 18, pp.705-762. Zbl0218.34046MR239221
34. G. R. SELL and Y. YOU (1988), Inertial manifolds : The non self adjoint case, Preprint. Zbl0760.34051
35. M. TABOADA (1988), Finite dimensional asymptotic behavior for the Swift-Hohenberg model of convection, Nonlinear Analysis, TMA, to appear. Zbl0707.58019MR1028246
36. R. TEMAM (1988), Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York. Zbl0662.35001MR953967

1. F. Demengel, J. M. Ghidaglia, Time-discretization and inertial manifolds