C1 approximations of inertial manifolds for dissipative nonlinear equations

Donald Jones, Edriss S. Titi

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

In this paper we study a class of nonlinear dissipative partial differential equations that have inertial manifolds. This means that the long-time behavior is equivalent to a certain finite system of ordinary differential equations. We investigate ways in which these finite systems can be approximated in the C1 sense. Geometrically this may be interpreted as constructing manifolds in phase space that are C1 close to the inertial manifold of the partial differential equation. Under such approximations the invariant hyperbolic sets of the global attractor persist.

Original languageEnglish (US)
Pages (from-to)54-86
Number of pages33
JournalJournal of Differential Equations
Volume127
Issue number1
DOIs
StatePublished - May 1 1996
Externally publishedYes

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Inertial Manifolds
Dissipative Equations
Nonlinear equations
Partial differential equations
Nonlinear Equations
Partial differential equation
Hyperbolic Set
Global Attractor
Long-time Behavior
Invariant Set
Approximation
System of Ordinary Differential Equations
Ordinary differential equations
Phase Space
Class

ASJC Scopus subject areas

  • Analysis

Cite this

C1 approximations of inertial manifolds for dissipative nonlinear equations. / Jones, Donald; Titi, Edriss S.

In: Journal of Differential Equations, Vol. 127, No. 1, 01.05.1996, p. 54-86.

Research output: Contribution to journalArticle

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