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

Başlangıç: 2017
Yayıncı: Erdal KARAPINAR

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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