Blow-up phenomena for solutions of discrete nonlinear p-Laplacian parabolic equations on networks

Abstract

This is an article to introduce discrete nonlinear p-Laplacian parabolic equations on networks and discuss the conditions under which blow-up occurs for the solutions. We first deal with the case p = 2, introducing a recent result about the blow-up phenomena for the solutions. Secondly, we deal with the general p-Laplacian case. In each case, we classify the parameters depending on the equations so that we can see when the solutions blow up or globally exist. Moreover, the blow-up time and blow-up rate are introduced for the blow-up solutions. The last part is devoted to the blow-up of Fujita type.