Adrien Blanchet, Jean Dolbeault, Benoit Perthame
Abstract: Submitted February 28, 2006. Published April 6, 2006.
Math Subject Classifications: 35B45, 35B30, 35D05, 35K15, 35B40, 35D10, 35K60.
Key Words: Keller-Segel model; existence; weak solutions;
free energy; entropy method; logarithmic Hardy-Littlewood-Sobolev
inequality; critical mass; Aubin-Lions compactness method;
hypercontractivity; large time behavior; time-dependent rescaling;
self-similar variables; intermediate asymptotics.
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Adrien Blanchet CEREMADE (UMR CNRS no. 7534), Université Paris Dauphine Place de Lattre de Tassigny, 75775 Paris Cédex 16, France and CERMICS, ENPC, 6-8 avenue Blaise Pascal Champs-sur-Marne, 77455 Marne-la-Vallée Cédex 2, France email: blanchet@ceremade.dauphine.fr http://www.ceremade.dauphine.fr/~blanchet/ | |
Jean Dolbeault CEREMADE (UMR CNRS no. 7534), Université Paris Dauphine Place de Lattre de Tassigny, 75775 Paris Cédex 16, France Phone: (33) 1 44 05 46 78, Fax: (33) 1 44 05 45 99 email: dolbeaul@ceremade.dauphine.fr http://www.ceremade.dauphine.fr/~dolbeaul/ | |
Benoît Perthame DMA (UMR CNRS no. 8553), Ecole Normale Supérieure 45 rue d'Ulm, 75005 Paris Cédex 05, France email: Benoit.Perthame@ens.fr http://www.dma.ens.fr/users/perthame |
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