Large time behavior of solutions to degenerate parabolic equations

Abstract

This paper deals with large time behavior of the Dirichlet problem to the degenerate parabolic equation \({u_t = g(u) \Delta u + f(u)}\) in a bounded domain \({\Omega \subset R^n}\) with smooth boundary \({\partial \Omega}\) . Under suitable conditions on f(u) and g(u), we show that all solutions will converge to the steady state exponentially.