Existence of solutions to a diffusive shallow medium equation

Verena Bögelein; Nicolas Dietrich; Matias Vestberg

doi:10.1007/s00028-020-00604-y

Existence of solutions to a diffusive shallow medium equation

Verena Bögelein, Nicolas Dietrich, Matias Vestberg^*

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

University of Salzburg

Research output: Contribution to journal › Article › Scientific › peer-review

6 Citations (Scopus)

64 Downloads (Pure)

Abstract

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.

Original language	English
Number of pages	45
Journal	Journal of Evolution Equations
Early online date	2020
DOIs	https://doi.org/10.1007/s00028-020-00604-y
Publication status	Published - 25 Jul 2020
MoE publication type	A1 Journal article-refereed

Keywords

Doubly nonlinear parabolic equations
Existence
Shallow medium equation

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Bögelein2020_Article_ExistenceOfSolutionsToADiffusiFinal published version, 491 KBLicence: CC BY

Cite this

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title = "Existence of solutions to a diffusive shallow medium equation",

abstract = "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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author = "Verena B{\"o}gelein and Nicolas Dietrich and Matias Vestberg",

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T1 - Existence of solutions to a diffusive shallow medium equation

AU - Bögelein, Verena

AU - Dietrich, Nicolas

AU - Vestberg, Matias

PY - 2020/7/25

Y1 - 2020/7/25

N2 - 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.

AB - 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.

KW - Doubly nonlinear parabolic equations

KW - Existence

KW - Shallow medium equation

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U2 - 10.1007/s00028-020-00604-y

DO - 10.1007/s00028-020-00604-y

M3 - Article

AN - SCOPUS:85088630321

SN - 1424-3199

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

ER -

Existence of solutions to a diffusive shallow medium equation

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