How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
Loading...
Date
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.