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SUMMARY:Explicit solvability and stability analysis of some particular sol
 utions in swarming models  - Stefan Martin 	(Imperial College\, London) 
DTSTART:20130620T135000Z
DTEND:20130620T124000Z
UID:TALK45891@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:In my talk I will present some recent advances in the study of
  particular solutions of kinetic equations related to swarming and focus o
 n a frequently used second-order self-propelled interacting particle syste
 m. It is well known that\, in the mean-field limit of the particle systems
 \, particular solutions such as flocks and rotating mills approach compact
 ly supported continuous solutions of the associated kinetic equation. The 
 explicit shape of spatial profiles of such solutions is generally unknown\
 , as is existence and uniqueness for general interaction potentials. I wil
 l first discuss results on one particular class of potentials\, so-called 
 Quasi-Morse potentials\, where explicit profiles and some uniqueness resul
 ts can be established. Secondly\, I will present a result on the stability
  of flock solutions in the second-order model for general potentials\, whi
 ch is given on the particle level.
LOCATION:MR12
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