Topological and ε-entropy for large volume limits of discretized parabolic equations

Gabriel J. Lord, Jacques Rougemont

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We consider semidiscrete and fully discrete approximations of nonlinear parabolic equations in the limit of unbounded domains, which by a scaling argument is equivalent to the limit of vanishing viscosity. We define the spatial density of e-entropy, topological entropy, and dimension for the attractors and show that these quantities are bounded. We also provide practical means of computing lower bounds on them. The proof uses the property that solutions lie in Gevrey classes of analyticity, which we define in a way that does not depend on the size of the spatial domain. As a specific example we discuss the complex Ginzburg-Landau equation.

Original languageEnglish
Pages (from-to)1311-1329
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume40
Issue number4
DOIs
Publication statusPublished - Sep 2002

Keywords

  • Dimension
  • Entropy
  • Large volume
  • Parabolic partial differential equations

Fingerprint Dive into the research topics of 'Topological and ε-entropy for large volume limits of discretized parabolic equations'. Together they form a unique fingerprint.

  • Cite this