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A nonlocal nonlinear diffusion equation with blowing up boundary conditions |
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| Authors: | M Bogoya R Ferreira JD Rossi |
| Institution: | a Departamento de Matemática, Universidad Católica de Chile, Santiago, Chile b Departamento de Matemática, Universidad Nacional de Colombia, Bogotá, Colombia c Departamento de Matemática Aplicada, Universidad Complutense de Madrid 28040, Spain d Departamento Matematica, FCEyN, UBA, Buenos Aires, Argentina |
| 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. |
| Keywords: | Nonlocal diffusion Neumann boundary conditions |
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