Seminario di Equazioni Differenziali e Applicazioni: Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction

Mercoledì 3 Febbraio 2016, ore 12:00 - Aula 1BC45 - Daniele Castorina



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Mercoledì 3 Febbraio 2016 alle ore 12:00 in Aula 1BC45, Daniele Castorina (Università di Padova) terrà un seminario dal titolo "Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction".

Replacing linear diffusion by a degenerate diffusion of porous medium type is known to regularize the classical two-dimensional parabolic-elliptic Keller-Segel model as in Calvez-Carrillo JMPA2006. The implications of nonlinear diffusion are that solutions exist globally and are uniformly bounded in time. We analyse the stationary case showing the existence of a unique, up to translation, global minimizer of the associated free energy. Furthermore, we prove that this global minimizer is a radially decreasing compactly supported continuous density function which is smooth inside its support, and it is characterized as the unique compactly supported stationary state of the evolution model. This unique profile is the clear candidate to describe the long time asymptotics of the diffusion dominated classical Keller-Segel model for general initial data.
This is a joint work with Jose Antonio Carrillo and Bruno Volzone.

Rif. Int. M. Bardi, C. Marchi, P. Mannucci.

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