Abstract

BOGOYA, MAURICIO  and  FORERO, ALBERTO. A semidiscrete model for a non-local diffusion equation with a source. Integración - UIS [online]. 2012, vol.30, n.2, pp.107-120. ISSN 0120-419X.

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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