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SUMMARY:Upper and lower bounds for the spatially homogeneous Landau equati
 on for Maxwellian molecules - Nualart\, E (Universit Paris 13 Nord)
DTSTART:20120913T110000Z
DTEND:20120913T115000Z
UID:TALK39729@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this talk we will introduce the spatially homogeneous Landa
 u equation for Maxwellian molecules\, widely studied by Villani and Desvil
 lettes\, among others. It is a non-linear partial differential equation wh
 ere the unknown function is the density of a gas in the phase space of all
  positions and velocities of particles. This equation is a common kinetic 
 model in plasma physics and is obtained as a limit of the Boltzmann equati
 on\, when all the collisions become grazing. We will first recall some kno
 wn results. Namely\, the existence and uniqueness of the solution to this 
 PDE\, as well as its probabilistic interpretation in terms of a non-linear
  diffusion due to Gurin. We will then show how to obtain Gaussian lower an
 d upper bound for the solution via probabilistic techniques. Joint work wi
 th Franois Delarue and Stphane Menozzi.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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