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 problemut=∑i=1N∂∂xi(ai(x, t, ∇u))−b(x, t, u),inΩ×(0, T),T>0∑i=1Nai(x, t, ∇u)ni=0,on∂Ω×(0, T)u(x, 0)=u0(x)x∈Ω,u0(x)⩾0inΩ,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.