Persistence of Invariant Sets for Dissipative Evolution Equations

Donald Jones, Andrew M. Stuart, Edriss S. Titi

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We show that results concerning the persistence of invariant sets of ordinary differential equations under perturbation may be applied directly to a certain class of partial differential equations. Our framework is particularly well-suited to encompass numerical approximations of these partial differential equations. Specifically, we show that for a class of PDEs with aC1inertial form, certain natural numerical approximations possess an inertial form close to that of the underlying PDE in theC1norm.

Original languageEnglish (US)
Pages (from-to)479-502
Number of pages24
JournalJournal of Mathematical Analysis and Applications
Volume219
Issue number2
DOIs
StatePublished - Mar 15 1998

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Dissipative Equations
Invariant Set
Numerical Approximation
Persistence
Partial differential equations
Evolution Equation
Partial differential equation
Ordinary differential equations
Ordinary differential equation
Perturbation
Class
Form
Framework

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Persistence of Invariant Sets for Dissipative Evolution Equations. / Jones, Donald; Stuart, Andrew M.; Titi, Edriss S.

In: Journal of Mathematical Analysis and Applications, Vol. 219, No. 2, 15.03.1998, p. 479-502.

Research output: Contribution to journalArticle

Jones, Donald ; Stuart, Andrew M. ; Titi, Edriss S. / Persistence of Invariant Sets for Dissipative Evolution Equations. In: Journal of Mathematical Analysis and Applications. 1998 ; Vol. 219, No. 2. pp. 479-502.
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