A nonlocal nonlinear diffusion equation with blowing up boundary conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:337

Article

Bogoya, M.^2,3  Ferreira, R.¹  Rossi, J. D.⁴ 

[1] Univ Complutense Madrid, Dept Matemat Aplicada, Madrid 28040, Spain

[2] Univ Nacl Colombia, Dept Matemat, Bogota, Colombia

[3] Catholic Univ Chile, Dept Matemat, Santiago, Chile

[4] UBA, FCEyN, Dept Matemat, Buenos Aires, DF, Argentina

关键词: nonlocal diffusion;    Neumann boundary conditions;   

DOI  :  10.1016/j.jmaa.2007.04.049

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free