The uniqueness of a nonlinear diffusion equation related to the p-Laplacian

Consider a nonlinear diffusion equation related to the p-Laplacian. Different from the usual evolutionary p-Laplacian equation, the equation is degenerate on the boundary due to the fact that the diffusion coefficient is dependent on the distance function. Not only the existence of the weak solution...

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Detalles Bibliográficos
Autor principal: Zhan, Huashui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5756294/
https://www.ncbi.nlm.nih.gov/pubmed/29367819
http://dx.doi.org/10.1186/s13660-017-1596-4
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author Zhan, Huashui
author_facet Zhan, Huashui
author_sort Zhan, Huashui
collection PubMed
description Consider a nonlinear diffusion equation related to the p-Laplacian. Different from the usual evolutionary p-Laplacian equation, the equation is degenerate on the boundary due to the fact that the diffusion coefficient is dependent on the distance function. Not only the existence of the weak solution is established, but also the uniqueness of the weak solution is proved.
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spelling pubmed-57562942018-01-22 The uniqueness of a nonlinear diffusion equation related to the p-Laplacian Zhan, Huashui J Inequal Appl Research Consider a nonlinear diffusion equation related to the p-Laplacian. Different from the usual evolutionary p-Laplacian equation, the equation is degenerate on the boundary due to the fact that the diffusion coefficient is dependent on the distance function. Not only the existence of the weak solution is established, but also the uniqueness of the weak solution is proved. Springer International Publishing 2018-01-05 2018 /pmc/articles/PMC5756294/ /pubmed/29367819 http://dx.doi.org/10.1186/s13660-017-1596-4 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zhan, Huashui
The uniqueness of a nonlinear diffusion equation related to the p-Laplacian
title The uniqueness of a nonlinear diffusion equation related to the p-Laplacian
title_full The uniqueness of a nonlinear diffusion equation related to the p-Laplacian
title_fullStr The uniqueness of a nonlinear diffusion equation related to the p-Laplacian
title_full_unstemmed The uniqueness of a nonlinear diffusion equation related to the p-Laplacian
title_short The uniqueness of a nonlinear diffusion equation related to the p-Laplacian
title_sort uniqueness of a nonlinear diffusion equation related to the p-laplacian
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5756294/
https://www.ncbi.nlm.nih.gov/pubmed/29367819
http://dx.doi.org/10.1186/s13660-017-1596-4
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