Modelo semidiscreto para una ecuación de
difusión no local con fuente

MAURICIO BOGOYA^*,    ALBERTO FORERO
Universidad Nacional de Colombia, Departamento de Matemáticas, Bogotá, Colombia.

Resumen. Estudiamos el modelo semidiscreto para un problema de difusión no local con fuente

con dato inicial Probamos la existencia y unicidad de las soluciones. Además, se demuestra que las soluciones del problema discreto convergen a las del continuo cuando el parámetro de la malla va a cero. Analizamos el fenómeno de explosión de las soluciones. Para algunas fuentes ƒ se obtiene la razón de explosión. Finalmente se presentan algunos experimentos numéricos.
Palabras Claves: difusión no local, condiciones de Neumann, semidiscretización, explosión.
MSC2010: 35K57, 35B40

Abstract. We study a discrete model for a non-local diffusion problem with a source, namely

with initial datum We prove the existence and uniqueness of the solution. Moreover, we show that solutions of discrete problem converge to the continuous ones when the mesh parameter goes to zero. We also study the blow-up phenomena of solutions. For some sources ƒ, we obtain the blow-up rate. Finally, we perform some numerical experiments.
Keywords: nonlocal diffusion, Neumann boundary conditions, semidiscretization, blow-up.

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^*Autor para correspondencia: E-mail: mbogoyal@unal.edu.co
Recibido: 17 de mayo de 2012, Aceptado: 20 de agosto de 2012.