Existence of weak solutions for a nonlinear parabolic equations by Topological degree

Authors : Mustapha AIT HAMMOU, Elhoussine AZROUL

Pages : 292-298

Doi:10.31197/atnaa.778533

View : 13 | Download : 7

Publication Date : 2020-12-30

Article Type : Research Paper

Abstract :We study the nonlinear parabolic initial boundary value problem associated to the equation ut − divainsert ignore into journalissuearticles values(x, t, u, grad u); = finsert ignore into journalissuearticles values(x, t);, where the terme − divainsert ignore into journalissuearticles values(x, t, u, grad u); is a Leray-Lions operator, The right-hand side f is assumed to belong to L^qinsert ignore into journalissuearticles values(Q);. We prove the existence of a weak solution for this problem by using the Topological degree theory for operators of the form L + S, where L is a linear densely defined maximal monotone map and S is a bounded demicontinuous map of class insert ignore into journalissuearticles values(S+); with respect to the domain of L.
Keywords : Nonlinear parabolic equations, Topological degree, Weak solution, map of class S,