Boundary fluxes for non-local diffusion

Details Boundary fluxes for non-local diffusion Boundary fluxes for non-local diffusion

2006-07-03

arxiv.org/abs/math/0607057v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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