Mercoledì 21 gennaio 2015 alle ore 14,30 presso la Sala delle Riunioni del Dipartimento (III piano) il Prof. Daniele Castorina  (Università degli Studi di Padova) terrà un seminario di analisi matematica 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 Josè Antonio Carrillo and Bruno Volzone.


N.B. La prima parte del seminario sarà introduttiva, adatta anche a pubblico non esperto.

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