Doubly nonlinear parabolic equations related to the p-Laplacian operator: Semi-discretization

Abstract

We study the doubly nonlinear parabolic equation ∂β(u) / ∂t - Δp u + f(x, t, u) = 0 in Ω x ℝ+, with Dirichlet boundary conditions and initial data. We investigate a time-discretization of the continuous problem by the Euler forward scheme. In addition to proving existence, uniqueness and stability questions, we study the long time behavior of the solution to the discrete problem. We prove the existence of a global attractor, and obtain its regularity under additional conditions.