- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 4 Issue: 4
- Existence of weak solutions for a nonlinear parabolic equations by Topological degree
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 : 5 | Download : 2
Publication Date : 2020-12-30
Article Type : Research
Abstract :We study the nonlinear parabolic initial boundary value problem associated to the equation ut − diva(x, t, u, grad u) = f(x, t), where the terme − diva(x, t, u, grad u) is a Leray-Lions operator, The right-hand side f is assumed to belong to L^q(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 (S+) with respect to the domain of L.Keywords : Nonlinear parabolic equations, Topological degree, Weak solution, map of class (S+)