Blow-Up Phenomenon for a Reaction–Diffusion Equation with Weighted Nonlocal Gradient Absorption Terms

This paper deals with the blow-up phenomenon of solutions to a reaction–diffusion equation with weighted nonlocal gradient absorption terms in a bounded domain. Based on the method of auxiliary function and the technique of modified differential inequality, we establish appropriate conditions on weight function and nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, upper and lower bounds for blow-up time are derived under appropriate measure in higher dimensional spaces.