A sharp condition for existence of an inertial manifold

Milan Miklavčič1
1Department of Mathematics, Michigan State University, East Lansing

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Tài liệu tham khảo

Babin, A. V., and Vishik, M. I. (1986). Unstable invariant sets of semigroups of nonlinear operators and their perturbations.Russ. Math. Surv. 41, 1–41.

Brunovský, P., and Tereščák, I. (1991). Regularity of invariant manifolds.J. Diff. Eq. 3, 313–337.

Chow, S.-N., and Lu, K. (1988). Invariant manifolds for flows in Banach spaces.J. Diff. Eq. 74, 285–317.

Foias, C., Sell, G. R., and Titi, E. S. (1989). Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations.J. Dynam. Diff. Eq. 1, 199–244.

Hale, J. K. (1988).Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr. 25, Am. Math. Soc., Providence.

Henry, D. (1981).Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., 840, Springer-Verlag, New York.

Mallet-Paret, J., and Sell, G. R. (1988). Inertial manifolds for reaction diffusion equations in higher space dimensions.J. Am. Math. Soc. 1, 805–866.

Matano, H. (1989). Personal communication.

Temam, R. (1988).Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York.

Vagi, S. (1969). A remark on Plancherel's theorem for Banach space valued functions.Ann. Scuola Norm. Sup. Pisa 23, 305–315.