Boundary fluxes for nonlocal diffusion
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Date
2007
Journal Title
Journal ISSN
Volume Title
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
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. (c) 2006 Elsevier Inc. All rights reserved.
Description
Keywords
nonlocal diffusion, boundary value problems, CAHN-HILLIARD EQUATION, CONVOLUTION MODEL, PHASE-TRANSITIONS, BLOW-UP