Uniform inertial sets for damped wave equations

P. Fabrie; C. Galusinski; A. Miranville

doi:10.3934/dcds.2000.6.393

Article Contents

2000, Volume 6, Issue 2: 393-418. Doi: 10.3934/dcds.2000.6.393

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Uniform inertial sets for damped wave equations

1.
Université de Bordeaux I, Laboratoire de Mathématiques Appliquées de Bordeaux, 351 cours de la libération, 33400 Talence
2.
Université de Bordeaux I, Laboratoire de Mathématiques Appliquées de Bordeaux, 351 Cours de la Libération, 33405 Talence Cedex
3.
Université de Poitiers, Département de Mathématiques, 40 Avenue du Recteur Pineau, 86022 Poitiers Cedex

Received: February 28, 1999

Revised: May 31, 1999

Published: March 2000

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Abstract

In this paper, we establish the existence of inertial sets for a class of wave equations in which the coefficient of the second order time derivative is $\varepsilon$. We show that the fractal dimension of these inertial sets does not depend on $\varepsilon$ for $\varepsilon$ small enough. We then compare the asymptotic behavior of the problem (as $\varepsilon\to 0$) through a continuity like property of the inertial sets. The autonomous case and nonautonomous case are studied.

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Mathematics Subject Classification: 35B40, 35B45, 35L05.

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