Extinction behavior for a parabolic $ p $-Laplacian equation with gradient source and singular potential

We concern with the extinction behavior of the solution for a parabolic $ p $-Laplacian equation with gradient source and singular potential. By energy estimate approach, Hardy-Littlewood-Sobolev inequality, a series of ordinary differential inequalities, and super-solution and sub-solution methods,...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 1; pp. 915 - 924
Main Authors Liu, Dengming, Yang, Luo
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
extinction
gradient source
parabolic p-laplacian equation
singular potential
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Summary:We concern with the extinction behavior of the solution for a parabolic $ p $-Laplacian equation with gradient source and singular potential. By energy estimate approach, Hardy-Littlewood-Sobolev inequality, a series of ordinary differential inequalities, and super-solution and sub-solution methods, we obtain the conditions on the occurrence of the extinction phenomenon of the weak solution.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022054