publication . Preprint . Article . 2006

How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems

Carmen Cortázar; Manuel Elgueta; Julio D. Rossi; Noemi Wolanski;
Open Access English
  • Published: 03 Jul 2006
  • 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.
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Subjects
free text keywords: Mathematics - Analysis of PDEs, 35K57, 35B40, Mechanical Engineering, Mathematics (miscellaneous), Analysis, Robin boundary condition, Mixed boundary condition, Heat equation, Diffusion equation, Neumann boundary condition, Boundary value problem, Poincaré–Steklov operator, Mathematics, Heat kernel, Mathematical analysis

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