Nonlinear stability and dynamical properties for a Kuramoto-Sivashinsky equation in space dimension two

Fred C. Pinto

doi:10.3934/dcds.1999.5.117

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1999, Volume 5, Issue 1: 117-136. Doi: 10.3934/dcds.1999.5.117

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Nonlinear stability and dynamical properties for a Kuramoto-Sivashinsky equation in space dimension two

Fred C. Pinto^1,

1.
Department of Mathematics, Indiana University, Bloomington, IN 47405

Received: October 31, 1997

Revised: March 31, 1998

Published: December 1998

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Abstract

Nonlinear stability and some other dynamical properties for a KS type equation in space dimension two are studied in this article. We consider here a variation of the KS equation where the derivatives in the nonlinear and the antidissipative linear terms are in one single direction. We prove the nonlinear stability for all positive times and study the corresponding attractor.

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Mathematics Subject Classification: 35B35, 35Q35, 34C35.

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Nonlinear stability and dynamical properties for a Kuramoto-Sivashinsky equation in space dimension two

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