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