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Type: Artigo de periódico
Title: Exponential Convergence Towards Stationary States For The 1d Porous Medium Equation With Fractional Pressure
Author: Carrillo J.A.
Huang Y.
Santos M.C.
Vazquez J.L.
Abstract: We analyse the asymptotic behaviour of solutions to the one dimensional fractional version of the porous medium equation introduced by Caffarelli and Vázquez [1,2], where the pressure is obtained as a Riesz potential associated with the density. We take advantage of the displacement convexity of the Riesz potential in one dimension to show a functional inequality involving the entropy, entropy dissipation, and the Euclidean transport distance. An argument by approximation shows that this functional inequality is enough to deduce the exponential convergence of solutions in self-similar variables to the unique steady states.
Editor: Academic Press Inc.
Rights: fechado
Identifier DOI: 10.1016/j.jde.2014.10.003
Date Issue: 2015
Appears in Collections:Unicamp - Artigos e Outros Documentos

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