Porous Medium Equation with Nonlocal Pressure

Diana Stan (), Félix Teso () and Juan Luis Vázquez ()
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Diana Stan: Basque Center for Applied Mathematics
Félix Teso: Norwegian University of Science and Technology
Juan Luis Vázquez: Universidad Autónoma de Madrid

A chapter in Current Research in Nonlinear Analysis, 2018, pp 277-308 from Springer

Abstract: Abstract We provide a rather complete description of the results obtained so far on the nonlinear diffusion equation u t = ∇⋅ (u m−1∇(−Δ)−s u), which describes a flow through a porous medium driven by a nonlocal pressure. We consider constant parameters m > 1 and 0 2, and the asymptotic behavior of solutions when N = 1. The cases m = 1 and m = 2 were rather well known.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-89800-1_12

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DOI: 10.1007/978-3-319-89800-1_12

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