Existence result for two-dimensional Kuramoto-Sivashinsky equation with nonlocal source

Abstract

We consider a nonlinear two-dimensional Kuramoto-Sivashinsky equation, with nonlocal source, and by a reduction method we determine a class of spatially periodic steady state solutions. Our analysis leads toward some computation, which can be easily automatized. By use of the symmetries of the problem we study the structure of the reduced equation, and we obtain an algebraic system of lower order, determining all the small solutions to the stationary problem. Mathematics Subject Classification: 34A34, 35B10, 74G20, 37G40