Quasilinear Parabolic Problem with p(x)-Laplacian Operator by Topological Degree

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Authors: M. A. HAMMOU

DOI: 10.46793/KgJMat2304.523H


We prove the existence of a weak solution for the quasilinear parabolic initial boundary value problem associated to the equation

u  −  Δ     u =  h,
  t     p(x)
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.


Quasilinear parabolic problems, variable exponents, topological degree, p(x)-Laplacian.


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