How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems

Details How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems

2006-07-03

arxiv.org/abs/math/0607058v1

Mathematics

Analysis of PDEs

Scientific paper

We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation with Neumann boundary conditions.

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