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SUMMARY:A kinetic flocking model with  diffusion - Renjun Duan\, RICAM (Li
 nz)
DTSTART:20091028T150000Z
DTEND:20091028T160000Z
UID:TALK21111@talks.cam.ac.uk
CONTACT:Alexander Lorz
DESCRIPTION:In this talk\, we consider the stability of the equilibrium st
 ates\nand the rate of convergence of solutions towards them for the\nconti
 nuous kinetic version of the Cucker-Smale flocking in presence\nof diffusi
 on whose strength depends on the density. This kinetic\nequation describes
  the collective behavior of an ensemble of\norganisms\, animals or devices
  which are forced to adapt their\nvelocities according to a certain rule i
 mplying a final\nconfiguration in which the ensemble flies at the mean vel
 ocity of\nthe initial configuration. Our analysis takes advantage both fro
 m\nthe fact that the global equilibrium is a Maxwellian distribution\nfunc
 tion\, and\, on the contrary to what happens in the Cucker-Smale\nmodel\, 
 the interaction potential is an integrable function. Precise\nconditions w
 hich guarantee polynomial rates of convergence towards\nthe global equilib
 rium are found. This is a joint work with M.\nFornasier and G. Toscani.
LOCATION:MR5\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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