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SUMMARY:Ground States for Diffusion Dominated Free Energies with Logarithm
 ic Interaction - Daniele Castorina (Università di Roma Tor Vergata)
DTSTART:20170501T140000Z
DTEND:20170501T150000Z
UID:TALK69645@talks.cam.ac.uk
CONTACT:Mikaela Iacobelli
DESCRIPTION:Replacing linear diffusion by a degenerate diffusion of porous
  medium type is known\nto regularize the classical two-dimensional parabol
 ic-elliptic Keller–Segel model [V. Calvez and J. A.\nCarrillo\, J. Math.
  Pures Appl. (9)\, 86 (2006)\, pp. 155–175]. The implications of nonline
 ar diffusion\nare that solutions exist globally and are uniformly bounded 
 in time. We analyze the stationary case\nshowing the existence of a unique
 \, up to translation\, global minimizer of the associated free energy.\nFu
 rthermore\, we prove that this global minimizer is a radially decreasing c
 ompactly supported continuous\ndensity function which is smooth inside its
  support\, and it is characterized as the unique\ncompactly supported stat
 ionary state of the evolution model. This unique profile is the clear cand
 idate\nto describe the long time asymptotics of the diffusion dominated cl
 assical Keller–Segel model\nfor general initial data. This is a joint wo
 rk with J.A. Carrillo (Imperial College\, London) and Bruno Volzone (Napol
 i Parthenope).
LOCATION:CMS\, MR13
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