Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 117 - 136, Volume 5, Issue 1, January 1999      doi:10.3934/dcds.1999.5.117

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Fred C. Pinto - Department of Mathematics, Indiana University, Bloomington, IN 47405, United States (email)

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.

Keywords:  Kuramoto-Sivashinsky equation, dissipative dynamics, attractors, existence of solutions.
Mathematics Subject Classification:   35B35, 35Q35, 34C35.

Received: November 1997;      Revised: April 1998;      Published: October 1998.