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Research Article | Open Access

On the global existence and extinction behavior for a polytropic filtration equation with variable coefficients

Dengming Liu, Changyu Liu( )
School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China
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Abstract

This article is devoted to the global existence and extinction behavior of the weak solution to an inhomogeneous polytropic filtration equation. Based on the integral norm estimate approach, the conditions on the global existence and the occurrence of the extinction singularity of the weak solution are given. Moreover, we also prove the non-extinction result under some appropriate assumptions by using the weak upper and lower solutions method.

Keywords

polytropic filtration equationglobal existenceextinction behaviornon-extinction phenomenonvariable coefficients

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Electronic Research Archive
Volume 30 Issue 2,
February 2022
Pages 425-439
DOI: 10.3934/era.2022022

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Liu D, Liu C. On the global existence and extinction behavior for a polytropic filtration equation with variable coefficients. Electronic Research Archive, 2022, 30(2): 425-439. https://doi.org/10.3934/era.2022022

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Received: 19 July 2021
Revised: 09 November 2021
Accepted: 14 November 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)