A nonlocal nonlinear diffusion equation with blowing up boundary conditions
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Date
2008
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ACADEMIC PRESS INC ELSEVIER SCIENCE
Abstract
We deal with boundary value problems (prescribing Dirichlet or Neumann boundary conditions) for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation. First, we prove existence, uniqueness and the validity of a comparison principle for these problems. Next, we impose boundary data that blow up in finite time and study the behavior of the solutions. (c) 2007 Published by Elsevier Inc.
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Keywords
nonlocal diffusion, Neumann boundary conditions, CONVOLUTION MODEL, PHASE-TRANSITIONS, LOCALIZATION, WAVES