Entropy solutions  for nonlinear parabolic problems involving the generalized $p(x)$-Laplace operator and $L^{1}$ data

Mohamed Badr Benboubker; Urbain Traoré

doi:10.5269/bspm.64565

Entropy solutions for nonlinear parabolic problems involving the generalized $p(x)$-Laplace operator and $L^{1}$ data

Autores

Mohamed Badr Benboubker Ecole National des Sciences Appliquées de Tétouan, Université Abdelmalek Essaadi,
Urbain Traoré

DOI:

https://doi.org/10.5269/bspm.64565

Resumo

In this paper we prove the existence of an entropy solution to nonlinear parabolic equations with nonhomogeneous Neumann boundary conditions and initial data in $L^{1}.$ By a time discretization technique we analyze the existence, the uniqueness and the stability questions. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.

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Publicado

2025-09-24

Edição

v. 43 (2025)

Seção

Artigos

Licença

When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).

The journal utilize the Creative Common Attribution (CC-BY 4.0).

Como Citar

Benboubker, M. B., & Traoré, U. (2025). Entropy solutions for nonlinear parabolic problems involving the generalized $p(x)$-Laplace operator and $L^{1}$ data. Boletim Da Sociedade Paranaense De Matemática, 43, 1-20. https://doi.org/10.5269/bspm.64565