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Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2009

Asymptotics of the fast diffusion equation via entropy estimates

Résumé

We consider non-negative solutions of the fast diffusion equation u_t=\Delta u^m with m\in(0,1), in the Euclidean space R^d, d \ge 3, and study the asymptotic behavior of a natural class of solutions, in the limit corresponding to t\to\infty for m \ge mc=(d-2)/d, or as t approaches the extinction time when m < mc. For a class of initial data we prove that the solution converges with a polynomial rate to a self-similar solution, for t large enough if m \ge mc, or close enough to the extinction time if m < mc. Such results are new in the range m \le mc where previous approaches fail. In the range mc
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Dates et versions

hal-00142404 , version 1 (18-04-2007)

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Adrien Blanchet, Matteo Bonforte, Jean Dolbeault, Gabriele Grillo, Juan-Luis Vázquez. Asymptotics of the fast diffusion equation via entropy estimates. Archive for Rational Mechanics and Analysis, 2009, 191, pp.347-385. ⟨hal-00142404⟩
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