publication . Article . Preprint . 2007

How to Approximate the Heat Equation with Neumann Boundary Conditions by Nonlocal Diffusion Problems

Noemi Wolanski; Julio D Rossi;
Open Access
  • Published: 03 Nov 2007 Journal: Archive for Rational Mechanics and Analysis, volume 187, pages 137-156 (issn: 0003-9527, eissn: 1432-0673, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
  • Country: Chile
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.
Subjects
free text keywords: Mechanical Engineering, Mathematics (miscellaneous), Analysis, Mathematics - Analysis of PDEs, 35K57, 35B40

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