Existence of global solutions and blow-up results for a class of p(x)−Laplacian heat equations with logarithmic nonlinearity-Reference-Cited by-同舟云学术

Existence of global solutions and blow-up results for a class of p(x)−Laplacian heat equations with logarithmic nonlinearity

Published:2023 Issue:22 Volume:37 Page:7527-7558
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Lalmi Abdellatif¹,Toualbia Sarra²,Laskri Yamina³

Affiliation:

1. Department of Mathematics, Faculty of Sciences, University of Badji Mokhtar-Annaba, Annaba, Algeria + Département des Mathématiques et Informatique, Faculté des Sciences et Technologie, Université de Ghardaia, Zone scientifique, Ghardaia, Algeria

2. Laboratory of mathematics, Informatics and Systems (LAMIS), Larbi Tebessi University, Tebessa, Algeria

3. Laboratory of Numerical Analysis and Optimization and Statistics (LANOS), University of Badji Mokhtar-Annaba, Annaba, Algeria + The Higher School of Industrial Technologies-Annaba, cité Safsaf, Annaba, Algeria

Abstract

This paper?s main objective is to examine an initial boundary value problem of a quasilinear parabolic equation of non-standard growth and logarithmic nonlinearity by utilizing the logarithmic Sobolev inequality and potential well method. Results of global existence, estimates of polynomial decay, and blowing up of weak solutions have been obtained under certain conditions that will be stated later. Our results extend those of a recent paper that appeared in the literature.

Publisher

National Library of Serbia

Reference41 articles.

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