Bifurcation of two-dimensional Kuramoto-Sivashinsky equation

Abstract

This paper deals with the steady state bifurcation of the K-S equation in two spatial dimensions with periodic boundary value condition and of zero mean. With the increase of parameter α, the steady state bifurcation behaviour can be very complicated. For convenience, only the cases α=2 and α=5 will be discussed. The asymptotic expressions of the steady state solutions bifurcated from the trivial solution near α=2 and α=5 are given. And the stability of the nontrival solutions bifurcated from α=2 is studied. Of course, the cases α=n 2+m 2,n,m∈N(α≠2,5) can be similarly discussed by the same method which is used to discussing the cases α=2 and α=5.