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

Abstract

<abstract><p>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.</p></abstract>