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On a class of nonlinear anisotropic parabolic problems
Journal article   Peer reviewed

On a class of nonlinear anisotropic parabolic problems

M. H. Abdou, M. Chrif, S. El Manouni and H. Hjiaj
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, Vol.146(1), pp.1-21
01/02/2016
DOI: https://doi.org/10.1017/S0308210515000402

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
We prove the existence of weak solutions for the strongly nonlinear parabolic problem u(t) + Au + g(x, t, u) + gamma vertical bar u vertical bar(p0) (- 2)u = f in the anisotropic Sobolev space L-p(0, T; W-0(1,p)(Omega)), where the data f are assumed to be in the dual, and the nonlinear term g( x, t, s) has growth and sign conditions on s.

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