dr. Castorina's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT

Daniele Castorina (UniPD)

Title: "Ground States for Diffusion Dominated Free Energies with 
Logarithmic Interaction"

Abstract: 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.

Venue: SISSA, Wednesday 10 February at 11:00 in lecture room 134