Existence of solutions to a diffusive shallow medium equation

In this article, we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First, we truncate the coefficients of the equation from above and below. Then, we prove convergence of the solutions of the truncated problem to a solution to the o...

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Detalles Bibliográficos
Autores principales: Bögelein, Verena, Dietrich, Nicolas, Vestberg, Matias
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550579/
https://www.ncbi.nlm.nih.gov/pubmed/34776772
http://dx.doi.org/10.1007/s00028-020-00604-y
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author Bögelein, Verena
Dietrich, Nicolas
Vestberg, Matias
author_facet Bögelein, Verena
Dietrich, Nicolas
Vestberg, Matias
author_sort Bögelein, Verena
collection PubMed
description In this article, we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First, we truncate the coefficients of the equation from above and below. Then, we prove convergence of the solutions of the truncated problem to a solution to the original equation.
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spelling pubmed-85505792021-11-10 Existence of solutions to a diffusive shallow medium equation Bögelein, Verena Dietrich, Nicolas Vestberg, Matias J Evol Equ Article In this article, we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First, we truncate the coefficients of the equation from above and below. Then, we prove convergence of the solutions of the truncated problem to a solution to the original equation. Springer International Publishing 2020-07-25 2021 /pmc/articles/PMC8550579/ /pubmed/34776772 http://dx.doi.org/10.1007/s00028-020-00604-y Text en © The Author(s) 2020 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Bögelein, Verena
Dietrich, Nicolas
Vestberg, Matias
Existence of solutions to a diffusive shallow medium equation
title Existence of solutions to a diffusive shallow medium equation
title_full Existence of solutions to a diffusive shallow medium equation
title_fullStr Existence of solutions to a diffusive shallow medium equation
title_full_unstemmed Existence of solutions to a diffusive shallow medium equation
title_short Existence of solutions to a diffusive shallow medium equation
title_sort existence of solutions to a diffusive shallow medium equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550579/
https://www.ncbi.nlm.nih.gov/pubmed/34776772
http://dx.doi.org/10.1007/s00028-020-00604-y
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