Blow-up Phenomena for a Reaction-diffusion Equation with Nonlocal Gradient Terms

Abstract

In this paper, we investigate blow-up phenomena of the solution to a reaction-diffusion equation with nonlocal gradient absorption terms under Robin boundary condition on a bounded star-shaped region. Based on the method of auxiliary function and the technique of modified differential inequality, we establish some conditions on the nonlinearities for which the solution exists globally or blows up at finite time, when the sign of the constant $\sigma$ is either positive or negative. Moreover, upper and lower bounds for a blow-up time are derived under appropriate measure in higher dimensional spaces.