@article{article_778533, title={Existence of weak solutions for a nonlinear parabolic equations by Topological degree}, journal={Advances in the Theory of Nonlinear Analysis and its Application}, volume={4}, pages={292–298}, year={2020}, DOI={10.31197/atnaa.778533}, author={Aıt Hammou, Mustapha and Azroul, Elhoussine}, keywords={Nonlinear parabolic equations, Topological degree, Weak solution, map of class (S+)}, 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.}, number={4}, publisher={Erdal KARAPINAR}