Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : We consider non-negative solutions of the fast diffusion equation u_t=Delta u^m with min(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 oinfty 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
 
 
Asymptotics of the fast diffusion equation via entropy estimates
BLANCHET Adrien, BONFORTE Matteo, DOLBEAULT Jean
GRILLO Gabriele, VAZQUEZ Juan-Luis
2007-13
19-04-2007
 
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