A quasilinear parabolic problem with a source term and a nonlocal absorption

Hui-Ling Li; Heng-Ling Wang; Xiao-Liu Wang

doi:10.3934/cpaa.2018092

Article Contents

2018, Volume 17, Issue 5: 1945-1956. Doi: 10.3934/cpaa.2018092

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A quasilinear parabolic problem with a source term and a nonlocal absorption

School of Mathematics, Southeast University, Nanjing 210096, China

* Corresponding author
* Corresponding author

Received: July 31, 2017

Revised: November 30, 2017

Published: April 2018

The first author is supported by the NSF of China 11171064. The third author is supported by the Postdoctoral Science Foundation of Jiangsu Province 1402026C, etc.

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Abstract

We investigate a quasi-linear parabolicproblem with nonlocal absorption, for which the comparison principle is not always available. Thesufficient conditions are established via energy method to guaranteesolution to blow up or not, and the long time behavior is alsocharacterized for global solutions.

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Mathematics Subject Classification: Primary: 35K57, 35K59; Secondary: 35B40, 35B44.

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