Well-posedness and numerical study for solutions of a parabolic equation with variable-exponent nonlinearities
type: Item
instance of: scholarly article
title: Well-posedness and numerical study for solutions of a parabolic equation with variable-exponent nonlinearities
zbMATH Open document ID: 1487.35226
DOI: 10.1155/2018/9754567
author: Jamal H. Al-Smail
author: Ala A. Talahmeh
author: Salim A. Messaoudi
published in: International Journal of Differential Equations
publication date: 2018-08-10T00:00:00Z
review text: Summary: We consider the following nonlinear parabolic equation: \(u_t - \operatorname{div}(| \nabla u |^{p(x) - 2} \nabla u) = f(x, t)\), where \(f : \Omega \times(0, T) \rightarrow \mathbb{R}\) and the exponent of nonlinearity \(p(\cdot)\) are given functions. By using a nonlinear operator theory, we prove the existence and uniqueness of weak solutions under suitable assumptions. We also give a two-dimensional numerical example to illustrate the decay of solutions.
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 6915965
zbMATH Keywords: nonlinear parabolic equation
zbMATH Keywords: existence and uniqueness of weak solutions
zbMATH Keywords: decay
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/9754567
OpenAlex ID: W2791445499
Wikidata QID: Q115243924
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description: scientific article; zbMATH DE number 6915965