¹Universidad Nacional de Colombia, Bogotá, Colombia. Email: mbogoyal@unal.edu.co
²Universidad Nacional de Colombia, Bogotá, Colombia. Email: cagomezsi@unal.edu.co

En este trabajo, probamos existencia y unicidad de soluciones, así como la validez de un principio de comparación para un modelo discreto asociado a un problema de difusión no local con condición de Neumann. Demostramos que las soluciones del modelo discreto convergen a las soluciones del modelo continuo cuando el parámetro de la malla va a cero. Finalmente mostramos algunos experimentos numéricos.

Palabras clave: Difusión no local, condiciones de Neumann, discretización, convergencia.

In this work we prove the existence and uniqueness of solutions as well as the validation of a comparison principle for a discrete model associated to a nonlocal diffusion problem with Neumann conditions. We show that the solutions for the discrete model converge to the solutions of the continuous model when the mesh parameter goes to zero. Finally, we perform some numerical experiments.

Key words: Nonlocal Diffusion, Neumann Boundary Conditions, Discretizations, Convergence.

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Referencias

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