Large Time Behavior of Solutions to a Class of Doubly Nonlinear Parabolic Equations

Abstract

We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation ut = div |u|m−1|∇u|p−2∇u in a cylinder Ω × R+, with initial condition u(x, 0) = u0(x) in Ω and vanishing on the parabolic boundary ∂Ω × R+. Here Ω is a bounded domain in RN , the exponents m and p satisfy m + p ≥ 3, p > 1, and the initial datum u0 is in L1(Ω).