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SUMMARY:Gamma-convergence of the Discrete Internal Energy and Application 
 to Gradient Flows - Francesco Patacchini (Imperial College)
DTSTART:20150225T160000Z
DTEND:20150225T170000Z
UID:TALK57703@talks.cam.ac.uk
CONTACT:Davide Piazzoli
DESCRIPTION:We want to approximate diffusion equations with finite numbers
  of particles. As the 2-Wasserstein energy functional for these equations 
 is not defined for point masses\, we spread uniformly the mass of each par
 ticle in some ball around it. This "tessellation" gives rise to a discrete
  energy functional well defined on point masses\, which we prove Gamma-con
 verges in the 2-Wasserstein topology to its continuum version as the numbe
 r of particles increases. For the linear diffusion case we use this result
  to show the convergence of the resulting discrete gradient flow to the he
 at equation. By a JKO scheme on the discrete gradient flow\, we show numer
 ical simulations. This is a joint work with J. A. Carrillo\, Y. Huang\, P.
  Sternberg and G. Wolansky.
LOCATION:MR14\, Centre for Mathematical Sciences
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