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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Communicated by P. Rabinowitz
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Cortazar, C., Elgueta, M., Rossi, J.D. et al. How to Approximate the Heat Equation with Neumann Boundary Conditions by Nonlocal Diffusion Problems. Arch Rational Mech Anal 187, 137–156 (2008). https://doi.org/10.1007/s00205-007-0062-8
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DOI: https://doi.org/10.1007/s00205-007-0062-8