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^*

^*Tämän työn vastaava kirjoittaja

Matematiikan ja systeemianalyysin laitos

University of Salzburg

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

6 Sitaatiot (Scopus)

64 Lataukset (Pure)

Abstrakti

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.

Alkuperäiskieli	Englanti
Sivumäärä	45
Julkaisu	Journal of Evolution Equations
Varhainen verkossa julkaisun päivämäärä	2020
DOI - pysyväislinkit	https://doi.org/10.1007/s00028-020-00604-y
Tila	Julkaistu - 25 heinäk. 2020
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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10.1007/s00028-020-00604-yLisenssi: CC BY

Bögelein2020_Article_ExistenceOfSolutionsToADiffusiFinal published version, 491 KBLisenssi: CC BY

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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.",

keywords = "Doubly nonlinear parabolic equations, Existence, Shallow medium equation",

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

year = "2020",

month = jul,

day = "25",

doi = "10.1007/s00028-020-00604-y",

language = "English",

journal = "Journal of Evolution Equations",

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TY - JOUR

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

UR - http://www.scopus.com/inward/record.url?scp=85088630321&partnerID=8YFLogxK

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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