On the convergence of attractors and exponential attractors for singularly perturbed hyperbolic equations

A. Eden, A. Milani

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper studies the dynamical behavior of parabolic equations under singular hyperbolic perturbations. In particular it is shown that for damped semilinear hyperbolic equations that are obtained as a singular perturbation of a parabolic equation, a finite dimensional global attractor exists and as the perturbation parameter tends to zero the attractor of the hyperbolic equation converges in some sense to the attractor of the corresponding parabolic partial differential equation. As the most challenging example, the authors treat throughout the paper the case of Klein-Gordon equation in three dimensional space when damping, which is inversely related to the perturbation parameter, is very large. (Authors)

Original languageEnglish
Pages (from-to)102-117
Number of pages16
JournalTurkish Journal of Mathematics
Volume19
Issue number1
Publication statusPublished - Jan 1 1995

Fingerprint

Exponential Attractors
Parameter Perturbation
Singularly Perturbed
Hyperbolic Equations
Parabolic Equation
Attractor
Klein-Gordon Equation
Semilinear Equations
Parabolic Partial Differential Equations
Global Attractor
Singular Perturbation
Dynamical Behavior
Damped
Damping
Tend
Perturbation
Converge
Three-dimensional
Zero

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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On the convergence of attractors and exponential attractors for singularly perturbed hyperbolic equations. / Eden, A.; Milani, A.

In: Turkish Journal of Mathematics, Vol. 19, No. 1, 01.01.1995, p. 102-117.

Research output: Contribution to journalArticle

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