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

Year 2020, Volume: 4 Issue: 4, 292 - 298, 30.12.2020

Mustapha Aıt Hammou , Elhoussine Azroul

https://doi.org/10.31197/atnaa.778533

Cited By: 1

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+)

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