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

U. Traoré

doi:10.4067/S0719-06462021000300385

DOI:

https://doi.org/10.4067/S0719-06462021000300385

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.

Keywords

Nonlinear parabolic problem , variable exponents , entropy solution , Neumann-type boundary conditions , semi-discretization

U. Traoré Laboratoire de Mathématiques et Informatique (LAMI), Université Joseph KI-ZERBO 03, BP 7021 Ouaga 03, Ouagadougou, Burkina Faso.

Pages: 385–409
Date Published: 2021-12-01
Vol. 23 No. 3 (2021)

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