Spectral barriers and inertial manifolds for dissipative partial differential equations

Peter Constantin, C. Foias, B. Nicolaenko, R. Témam

Research output: Contribution to journalArticle

72 Scopus citations

Abstract

In recent years, the theory of inertial manifolds for dissipative partial differential equations has emerged as an active area of research. An inertial manifold is an invariant manifold that is finite dimensional, Lipschitz, and attracts exponentially all trajectories. In this paper, we introduce the notion of a spectral barrier for a nonlinear dissipative partial differential equation. Using this notion, we present a proof of existence of inertial manifolds that requires easily verifiable conditions, namely, the existence of large enough spectral barriers.

Original languageEnglish (US)
Pages (from-to)45-73
Number of pages29
JournalJournal of Dynamics and Differential Equations
Volume1
Issue number1
DOIs
StatePublished - Jan 1 1989

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Spectral barriers
  • dissipation
  • inertial manifolds

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