¹Universidad Nacional de Colombia, Bogotá, Colombia. Email: mbogoyal@unal.edu.co

We study the initial-value problem prescribing Neumann boundary conditions for a nonlocal nonlinear diffusion operator with source, in a bounded domain in 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.

Key words: Nonlocal diffusion, Neumann boundary conditions, Blow-up.

Se estudia el problema de valor inicial con condiciones de Neumann para un operador no lineal de difusión no local con fuente, en un dominio acotado en R^N con frontera suave. Se demuestra la existencia y unicidad de las soluciones y se da un principio de comparación para las soluciones. Se analiza el fenómeno de explosión. La razón de explosión es dada para algunas fuentes particulares.

Palabras clave: Difusión no local, condiciones de Neumann, explosión.

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