Explicit Barenblatt profiles for fractional porous medium equations

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 10 Jun 2014Embargo end date: 01 Jan 2013 United Kingdom English Publisher:WileyJournal:Bulletin of the London Mathematical Society, volume 46, pages 857-869 (issn: 0024-6093,

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Authors: Huang, Y;

doi: 10.1112/blms/bdu045 , 10.48550/arxiv.1312.0469

arXiv: 1312.0469

handle: 10044/1/17775

Explicit Barenblatt profiles for fractional porous medium equations

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Abstract

Several one-parameter families of explicit self-similar solutions are constructed for the porous medium equations with fractional operators. The corresponding self-similar profiles, also called \emph{Barenblatt profiles}, have the same forms as those of the classic porous medium equations. These new exact solutions complement current theoretical analysis of the underlying equations and are expected to provide insights for further quantitative investigations.

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United Kingdom

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Keywords

self-similar solutions, Flows in porous media; filtration; seepage, fractional porous medium equation, Barenblatt profile, 35C06, Fractional partial differential equations, fractional Laplace operator, Classical hypergeometric functions, \({}_2F_1\), Mathematics - Analysis of PDEs, Reaction-diffusion equations, FOS: Mathematics, Self-similar solutions to PDEs, hypergeometric functions, Analysis of PDEs (math.AP)

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