Existence and Regularity of a Global Attractor for Doubly Nonlinear Parabolic Equations

Abstract

In this paper we consider a doubly nonlinear parabolic partial differential equation ∂β(u)/ ∂t - Δpu + ƒ(x, t, u) = 0 in Ω x ℝ+, with Dirichlet boundary condition and initial data given. We prove the existence of a global compact attractor by using a dynamical system approach. Under additional conditions on the nonlinearities β, ƒ, and on p, we prove more regularity for the global attractor and obtain stabilization results for the solutions.