Regularity of the attractor for symmetric regularized wave equation

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December 2005, 4(4): 695-704. doi: 10.3934/cpaa.2005.4.695

Regularity of the attractor for symmetric regularized wave equation

1.	LAMFA CNRS UMR 6140,Universite de Picardie Jules Verne,33, rue Saint-Leu, 80039 Amiens, Universite Cadi Ayyad, Faculte des Sciences et Techniques, Avenue Abdelkrim Khattabi, BP 618, Marrakech, Maroc, France

Received December 2004 Revised May 2005 Published September 2005

Abstract
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In this article we study the long time behavior of the solutions to dissipative generalized symmetric regularized long wave equations with damping. We prove that the long time behavior is described by a compact attractor which captures all trajectories in $ H^1\times L^2$. We moreover establish that the attractor $\mathcal A$ is a compact set in $ H^2\times H^1$.

Keywords: global attractor, Symmetric regularized wave equation, regularity of the attractor..

Mathematics Subject Classification: 37C45.

Citation: Abdelghafour Atlas. Regularity of the attractor for symmetric regularized wave equation. Communications on Pure & Applied Analysis, 2005, 4 (4) : 695-704. doi: 10.3934/cpaa.2005.4.695

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