Discrete gevrey regularity, attractors and upper-semicontinuity for a finite difference approximation to the Ginzburg-Landau equation

G J Lord, A M Stuart

Research output: Contribution to journalArticle

Abstract

A semi-discrete spatial finite difference approximation to the complex Ginzburg-Landau equation with cubic non-linearity is considered. Using the fractional powers of a sectorial operator, discrete versions of the Sobolev spaces H-s, and Gevrey classes of regularity tau, G(tau), are introduced. Discrete versions of some standard Sobolev space norm inequalities are proved.

Original languageEnglish
Pages (from-to)1003-1047
Number of pages45
JournalNumerical Functional Analysis and Optimization
Volume16
Issue number7-8
DOIs
Publication statusPublished - 1995

Keywords

  • NAVIER-STOKES EQUATIONS
  • CONVERGENCE
  • DYNAMICS
  • SYSTEM

Cite this

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abstract = "A semi-discrete spatial finite difference approximation to the complex Ginzburg-Landau equation with cubic non-linearity is considered. Using the fractional powers of a sectorial operator, discrete versions of the Sobolev spaces H-s, and Gevrey classes of regularity tau, G(tau), are introduced. Discrete versions of some standard Sobolev space norm inequalities are proved.",
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AU - Stuart, A M

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N2 - A semi-discrete spatial finite difference approximation to the complex Ginzburg-Landau equation with cubic non-linearity is considered. Using the fractional powers of a sectorial operator, discrete versions of the Sobolev spaces H-s, and Gevrey classes of regularity tau, G(tau), are introduced. Discrete versions of some standard Sobolev space norm inequalities are proved.

AB - A semi-discrete spatial finite difference approximation to the complex Ginzburg-Landau equation with cubic non-linearity is considered. Using the fractional powers of a sectorial operator, discrete versions of the Sobolev spaces H-s, and Gevrey classes of regularity tau, G(tau), are introduced. Discrete versions of some standard Sobolev space norm inequalities are proved.

KW - NAVIER-STOKES EQUATIONS

KW - CONVERGENCE

KW - DYNAMICS

KW - SYSTEM

U2 - 10.1080/01630569508816658

DO - 10.1080/01630569508816658

M3 - Article

VL - 16

SP - 1003

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JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

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