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

C. Cortazar·M. Elgueta·J. D. Rossi·N. Wolanski
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Abstract

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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C. Cortazar, M. Elgueta, J. D. Rossi, N. Wolanski. 2006-07-03. How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems. https://arxiv.org/abs/math/0607058

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