Existence of Weak Solutions to a Class of Nonlinear Degenerate Parabolic Equations in Weighted Sobolev Space Mohamed El Ouaarabi, Chakir Allalou and Said Melliani

Abstract

In this work, we prove the existence of a weak solutions for the initial boundary value problem associated with the nonlinear degenerate parabolic equationsWe will use the Topological degree theory for operators of the type T + S, where S is a bounded demicontinuous map of type (S + ) and T is a linear densely defined maximal monotone map with respect to a domain of T , and we study this problem in the space L p (0, T ; W 1,p 0 (Ω, ω)), where Ω is a bounded domain in R N (N ≥ 2), p ≥ 2 and ω is a vector of weight functions.