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SUMMARY:On asymptotic gradient flow structures of PDE models with excluded
  volume effects - Marie-Therese Wolfram (University of Warwick)
DTSTART:20180111T160000Z
DTEND:20180111T170000Z
UID:TALK93358@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:We discuss the analysis of a cross-diffusion PDE system for mi
 xtures of hard spheres\, which was derived by Bruna and Chapman (J Chem Ph
 ys 137\, 2012) from a stochastic system of interacting Brownian particles 
 using the methods of matched asymptotics. While the system has a gradient 
 flow structure in the symmetric case of all particles having the same size
  and diffusivity\, this is not valid in general. For the general case\, we
  introduce the concept of an asymptotic gradient flow structure and show h
 ow it can be used to study the behavior close to equilibrium. To gain furt
 her insights into the dynamics of asymptotic gradient flows\, we study the
  system in the special case of two specific species – namely diffusing (
 Brownian) and immobile (obstacle) particles. In this case the cross-diffus
 ion system reduces to a single nonlinear nonlinear Fokker--Planck equation
 \, which again has no full gradient flow structure. However it can be inte
 rpreted as an asymptotic gradient flow for \ndifferent entropy and mobilit
 y pairs. We discuss several possible such pairs and present global in time
  existence results as well as study the long time behavior of the correspo
 nding full gradient flow equation. Furthermore we illustrate the dynamics 
 of the different equations with numerical simulations.\n\nThis is joint wo
 rk with M. Bruna (Oxford)\, M. Burger (Münster) and H. Ranetbauer (Vienna
 )
LOCATION:MR 14\, CMS
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