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Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions

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Abstract

We present a model for nonlocal diffusion with Dirichlet boundary conditions in a bounded smooth domain. We prove that solutions of properly rescaled nonlocal problems approximate uniformly the solution of the corresponding Dirichlet problem for the classical heat equation.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Catolica de Chile, Casilla 306, Correo 22, Santiago, Chile

    Carmen Cortazar & Manuel Elgueta

  2. Departamento de Matemática, FCEyN UBA (1428), Buenos Aires, Argentina

    Julio D. Rossi

Authors
  1. Carmen Cortazar
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  2. Manuel Elgueta
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  3. Julio D. Rossi
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Correspondence to Carmen Cortazar.

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Cortazar, C., Elgueta, M. & Rossi, J.D. Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions. Isr. J. Math. 170, 53–60 (2009). https://doi.org/10.1007/s11856-009-0019-8

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  • DOI: https://doi.org/10.1007/s11856-009-0019-8

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