Archive for Rational Mechanics and Analysis

, Volume 187, Issue 1, pp 137–156 | Cite as

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

  • Carmen Cortazar
  • Manuel Elgueta
  • Julio D. Rossi
  • Noemi Wolanski
Article

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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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Carmen Cortazar
    • 1
  • Manuel Elgueta
    • 1
  • Julio D. Rossi
    • 2
  • Noemi Wolanski
    • 2
  1. 1.Departamento de MatemáticaUniversidad Catolica de ChileSantiagoChile
  2. 2.Departamento de MatemáticaFCEyN, UBA, Ciudad Universitaria, Pab IBuenos AiresArgentina

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