publication . Preprint . 2006

Boundary fluxes for non-local diffusion

Cortazar, C.; Elgueta, M.; Rossi, J. D.; Wolanski, N.;
Open Access English
  • Published: 03 Jul 2006
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.
free text keywords: Mathematics - Analysis of PDEs, 35K57, 35B40
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