Asymptotic behavior for parabolic equations with interior degeneracy

Abstract

The long time behavior of a class of degenerate parabolic equations in a bounded domain will be considered in the sense that the nonnegative diffusion coefficient a(x) is allowed to vanish in a set of positive measure in the interior of the domain. We prove decay rates for a class of semilinear reaction diffusion equations and a nonlinear equation governed by the p-Laplacian, for p>2.