arXiv:1001.0410 Abstract | arXiv Analytics

arXiv:1001.0410 [math.AP]Abstract References Reviews Resources

Nonlinear porous medium flow with fractional potential pressure

Published 2010-01-03, updated 2010-02-01Version 2

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.

Comments: 32 pages, Latex

DOI: 10.1007/s00205-011-0420-4

Categories: math.AP

Subjects: 35K55, 35K65

Keywords: nonlinear porous medium flow, fractional potential pressure, inverse fractional laplacian operator, nonlocal diffusion effects, fractional diffusion models

Tags: journal article

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