Attractive invariant manifolds under approximation. Inertial manifolds

Don A. Jones, Andrew M. Stuart

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

A class of nonlinear dissipative partial difTcrential equations that possess finite dimensional attractive invariant manifolds is considered An existence and perturba-tion theory is developed which unifies the cases of unstable manifolds and inertialmanifolds into a single framework. It is shown that certain approximations of theseequations, such as those arising from spectral or finite element methods in space, one-step lime-discreti/ation or a combination of both, also have attractive invariantmanifolds. Convergence of the approximate manifolds to the true manifolds isestablished as the approximation is refined. In this part of the paper applicationsto the behavior of inertial manifolds under approximation are considered. Fromthis analysis deductions about the structure of the attractor and the flow on theattractor under discretization can be made.

Original languageEnglish (US)
Pages (from-to)588-637
Number of pages50
JournalJournal of Differential Equations
Volume123
Issue number2
DOIs
StatePublished - Dec 1995
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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