A complete characterization of Fujita's blow-up solutions for discrete p-Laplacian parabolic equations under the mixed boundary conditions on networks

Abstract

In this paper, we study long-time behaviors of solutions to the discrete p-Laplacian parabolic equations with time-dependent reactionsut=Δp,ωu+ψ(t)|u|q−1u with nontrivial and nonnegative initial data, under the mixed boundary conditions, where p≥2, q>0, and ψ is a positive continuous function. The goal of this paper is to characterize completely the parameters p, q, and function ψ to see when the solutions are Fujita's blow-up solutions, general blow-up solutions, or global solutions.