Asymptotic stability for nonlinear degenerate parabolic equations with Neumann boundary conditions (Q1175620)

Consider the problem: \(u_ t-\Delta\tilde\beta=f\), \(\tilde\beta\in\beta(u)\) in \(\mathbb{R}\times\Omega\), \(\partial_ n\tilde\beta=h\) on \(\mathbb{R}\times\partial\Omega\) where \(\Omega\subset\mathbb{R}^ N\) is a bounded domain, \(\beta\) is a given maximal monotone graph in \(\mathbb{R}\times\mathbb{R}\); \(f\), \(h\) are given functions. The author proves existence of a periodic weak solution and asymptotic stability of certain solutions as \(t\to\infty\). Further, periodicity of solutions defined on \(\mathbb{R}\) is shown.