Reminder: 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