The Stability Of Nonlinear Kuramoto-Sivashinsky Equation

In this paper,we rmainly study the stability of nonlinear Kuramoto-Sivashinsky equation:(?)where the parameter v is a positive constant.Define (?).First we use Lumer-Philips theorem to obtain A generates a contraction semigroup S(t).Consequently,we use separation of variables to get the eigenvalues of A and the corresponding eigenvectors,and the specific form of semigroup S(t)is expressed.Using Banach contraction fixed point theorem,the system is asymptoti-cally stable when v>1.