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Asymptotic behavior of nonlinear diffusions

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2003 France Publisher:International Press of BostonJournal:Mathematical Research Letters, volume 10, pages 551-557 (issn: 1073-2780, eissn: 1945-001X,

Authors: Dolbeault, Jean; del Pino, Manuel;

doi: 10.4310/mrl.2003.v10.n4.a13 , 10.5281/zenodo.1346378 , 10.5281/zenodo.1346379

Asymptotic behavior of nonlinear diffusions

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Abstract

We describe the asymptotic behavior as t → ∞ of the solution of ut = ∆pu in IRN, for (2N +1)/(N +1) ≤ p < N and non-negative, integrable initial data. Optimal rates in Lq , q = 2 − 1/(p − 1) for the convergence towards a self-similar profile corresponding to a solution with Dirac distribution initial data are found. They are connected with optimal constants for a Gagliardo-Nirenberg inequality.

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France

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Keywords

Dirac distribution, 515, Asymptotic behavior of solutions to PDEs, asymptotic behavior, Initial value problems for second-order parabolic equations, Analyse, Degenerate parabolic equations, self-similar profile, Gagliardo-Nirenberg inequality, 510

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