Blow-up Analysis for a Nonlocal Reaction-diffusion Equation with Robin Boundary Conditions

Abstract

This work is concerned with the blow-up phenomena for a nonlocal reaction-diffusion equation with null Robin boundary conditions. We establish sufficient conditions to guarantee the solution exists globally or blows up at finite time under appropriate measure sense. Moreover, upper and lower bounds for the blow-up time are derived in higher dimensional spaces. Finally, some application examples are presented.