Blow-up estimate in a reaction–diffusion equation with nonlinear nonlocal flux and source

Abstract

This paper deals with a reaction–diffusion equation with nonlocal inner source and nonlocal boundary flux. Besides the influence of exponents, we find out that the weighted functions and the measure of the domain could lead to the existence of global solutions for any initial data. Larger weighted functions require smaller initial data in guaranteeing the existence of global solutions to the problem. Blow-up rates are obtained under different dominations of nonlinearities in one dimensional space. The upper and lower bounds of blow-up time are determined for all spatial dimensions, respectively. Moreover, the solutions blow up only on the boundary when the nonlocal flux dominates the blow-up.