How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
Analysis of PDEs
2007-05-23 v1
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.
Cite
@article{arxiv.math/0607058,
title = {How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems},
author = {C. Cortazar and M. Elgueta and J. D. Rossi and N. Wolanski},
journal= {arXiv preprint arXiv:math/0607058},
year = {2007}
}