1999, 5(1): 117-136. doi: 10.3934/dcds.1999.5.117

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

1. 

Department of Mathematics, Indiana University, Bloomington, IN 47405, United States

Received  November 1997 Revised  April 1998 Published  October 1998

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.
Citation: Fred C. Pinto. Nonlinear stability and dynamical properties for a Kuramoto-Sivashinsky equation in space dimension two. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 117-136. doi: 10.3934/dcds.1999.5.117
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