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February 2007 Semidiscretization and Long-time Asymptotics of Nonlinear Diffusion Equations
José A. Carrillo, Marco Di Francesco, Maria P. Gualdani
Commun. Math. Sci. 5(S1): 21-53 (February 2007).


We review several results concerning the long-time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analyzed. We demonstrate the long-time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities near zero.


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José A. Carrillo. Marco Di Francesco. Maria P. Gualdani. "Semidiscretization and Long-time Asymptotics of Nonlinear Diffusion Equations." Commun. Math. Sci. 5 (S1) 21 - 53, February 2007.


Published: February 2007
First available in Project Euclid: 5 April 2007

zbMATH: 1145.35028
MathSciNet: MR2301287

Primary: 35B40 , 35K55 , 35K65

Keywords: long-time asymptotics , mass transport methods , Nonlinear diffusion

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. S1 • February 2007
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