Blow-up for a nonlocal nonlinear diffusion equation with source

Abstract

We study the initial-value problem prescribing Neumann boundary conditions for a nonlocal nonlinear diffusion operator with source, in a bounded domain in $\mathbb{R}^N$ with a smooth boundary. We prove existence, uniqueness of solutions and we give a comparison principle for its solutions. The blow-up phenomenon is analyzed. Finally, the blow up rate is given for some particular sources.