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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Fokker-Planck models for Bose-Einstein particles -
Toscani\, G (Pavia)
DTSTART;TZID=Europe/London:20100909T163000
DTEND;TZID=Europe/London:20100909T173000
UID:TALK26073AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/26073
DESCRIPTION:We study nonnegative\, measure-valued solutions of
the initial value problem for one-dimensional dri
ft-diffusion equations where the linear drift has
a driving potential with a quadratic growth at inf
inity\, and the nonlinear diffusion is governed by
an increasing continuous and bounded function. Th
e initial value problem is studied in corresponden
ce to initial densities that belong to the space o
f nonnegative Borel measures with finite mass and
finite quadratic momentum and it is the gradient f
low of a suitable entropy functional with respect
to the Wasserstein distance. Due to the degeneracy
of diffusion for large densities\, concentration
of masses can occur\, whose support is transported
by the drift. We shall show that the large-time b
ehavior of solutions depends on a critical mass wh
ich can be explicitly characterized in terms of th
e diffusion function and of the drift term. If the
initial mass is less than the critical mass\, the
entropy has a unique minimizer which is absolutel
y continuous with respect to the Lebesgue measure.
Conversely\, when the total mass of the solutions
is greater than the critical one\, the steady sta
te has a singular part in which the exceeding mass
is accumulated.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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