English

Boundary fluxes for non-local diffusion

Analysis of PDEs 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0607057,
  title  = {Boundary fluxes for non-local diffusion},
  author = {C. Cortazar and M. Elgueta and J. D. Rossi and N. Wolanski},
  journal= {arXiv preprint arXiv:math/0607057},
  year   = {2007}
}