English

Nonlinear porous medium flow with fractional potential pressure

Analysis of PDEs 2015-05-14 v2

Abstract

We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove existence of a weak and bounded solution that propagates with finite speed, a property that is nor shared by other fractional diffusion models.

Keywords

Cite

@article{arxiv.1001.0410,
  title  = {Nonlinear porous medium flow with fractional potential pressure},
  author = {Luis A. Caffarelli and Juan L. Vazquez},
  journal= {arXiv preprint arXiv:1001.0410},
  year   = {2015}
}

Comments

32 pages, Latex