Bifurcation and Stability of Nontrivial Solution to Kuramoto-Sivashinsky Equation

This paper deals with the steady-state bifurcation of the Kuramoto-Sivashinsky equation in one space dimension with periodic botmdary condition and of zero mean. The asymptotic expressions of the steady-state solutions biftlrcated from the trivial solution are given. Furthermore, the stability of the nontrivial solutions are discussced.