Large Time Behavior of Solutions to the Neumann Problem for a Quasilinear Second Order Degenerate Parabolic Equation in Domains with Noncompact Boundary

We investigate the optimal rate of stabilization at large time of a solution to the Neumann problem u(x, 0)=u0(x) x Ω, u0(x) 0 in Ω,where Ω RN, N 2, is an unbounded domain with sufficiently smooth noncompact boundary ∂Ω satisfying certain isoperimetrical inequality and n=(ni) is the outward normal to ∂Ω.