Entropy solution for a nonlinear parabolic problem with homogeneous Neumann boundary condition involving variable exponents

  • U. Traoré Laboratoire de Mathématiques et Informatique (LAMI), Université Joseph KI-ZERBO 03, BP 7021 Ouaga 03, Ouagadougou, Burkina Faso.
Keywords: Nonlinear parabolic problem, variable exponents, entropy solution, Neumann-type boundary conditions, semi-discretization

Abstract

In this paper we prove the existence and uniqueness of an entropy solution for a non-linear parabolic equation with homogeneous Neumann boundary condition and initial data in \(L^1\). By a time discretization technique we analyze the existence, uniqueness and stability questions. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.

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Published
2021-12-01
How to Cite
[1]
U. Traoré, “Entropy solution for a nonlinear parabolic problem with homogeneous Neumann boundary condition involving variable exponents”, CUBO, vol. 23, no. 3, pp. 385–409, Dec. 2021.
Section
Articles