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

Dengming Liu; Changyu Liu; Dengming Liu; Changyu Liu

doi:10.3934/era.2022022

Electronic Research Archive

2022, Volume 30, Issue 2: 425-439. doi: 10.3934/era.2022022

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Research article

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

Received: 19 July 2021 Revised: 09 November 2021 Accepted: 14 November 2021 Published: 18 January 2022

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.
- polytropic filtration equation,
- global existence,
- extinction behavior,
- non-extinction phenomenon,
- variable coefficients
Citation: Dengming Liu, Changyu Liu. On the global existence and extinction behavior for a polytropic filtration equation with variable coefficients[J]. Electronic Research Archive, 2022, 30(2): 425-439. doi: 10.3934/era.2022022

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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.

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