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.
Citation: Ling Zhou, Zuhan Liu. Blow-up in a $ p $-Laplacian mutualistic model based on graphs[J]. AIMS Mathematics, 2023, 8(12): 28210-28218. doi: 10.3934/math.20231444
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.
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Ling Zhou, Zuhan Liu. Blow-up in a $ p $-Laplacian mutualistic model based on graphs[J]. AIMS Mathematics, 2023, 8(12): 28210-28218. doi: 10.3934/math.20231444
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