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SUMMARY:Fokker-Planck models for Bose-Einstein particles - Toscani\, G (Pa
 via)
DTSTART:20100909T153000Z
DTEND:20100909T163000Z
UID:TALK26073@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We study nonnegative\, measure-valued solutions of the initial
  value problem for one-dimensional drift-diffusion equations where the lin
 ear drift has a driving potential with a quadratic growth at infinity\, an
 d the nonlinear diffusion is governed by an increasing continuous and boun
 ded function. The initial value problem is studied in correspondence to in
 itial densities that belong to the space of nonnegative Borel measures wit
 h finite mass and finite quadratic momentum and it is the gradient flow of
  a suitable entropy functional with respect to the Wasserstein distance. D
 ue to the degeneracy of diffusion for large densities\, concentration of m
 asses can occur\, whose support is transported by the drift. We shall show
  that the large-time behavior of solutions depends on a critical mass whic
 h can be explicitly characterized in terms of the diffusion function and o
 f the drift term. If the initial mass is less than the critical mass\, the
  entropy has a unique minimizer which is absolutely continuous with respec
 t to the Lebesgue measure. Conversely\, when the total mass of the solutio
 ns is greater than the critical one\, the steady state has a singular part
  in which the exceeding mass is accumulated.
LOCATION:Seminar Room 1\, Newton Institute
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