Blow-up in a $ p $-Laplacian mutualistic model based on graphs

In this paper, we study a $ p\, $-Laplacian ($ p > 2 $) reaction-diffusion system based on weighted graphs that is used to describe a network mutualistic model of population ecology. After overcoming difficulties caused by the nonlinear $ p\, $-Laplacian, we develop a new strong mutualistic condi...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 12; pp. 28210 - 28218
Main Authors Zhou, Ling, Liu, Zuhan
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
blow-up
comparison principle
laplacian
network
p
strong mutualistic systems
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ISSN2473-6988
2473-6988
DOI10.3934/math.20231444

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Summary:In this paper, we study a $ p\, $-Laplacian ($ p > 2 $) reaction-diffusion system based on weighted graphs that is used to describe a network mutualistic model of population ecology. After overcoming difficulties caused by the nonlinear $ p\, $-Laplacian, we develop a new strong mutualistic condition, and the blow-up properties of the solution for any nontrivial initial data are proved under this condition. In this sense, we extend the blow-up results of models with a graph Laplacian ($ p = 2 $) to a general graph $ p\, $-Laplacian.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20231444