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SUMMARY:Non linear problems involving non local diffusions - Professor Lui
 s Caffarelli\, University of Texas at Austin
DTSTART:20110428T110000Z
DTEND:20110428T120000Z
UID:TALK30469@talks.cam.ac.uk
CONTACT:Amy Dittrich
DESCRIPTION:Diffusion is a very common model for motion in physics\, chemi
 stry\, biology and in the social sciences. Typically\, populations of part
 icles or molecules\, or individuals tend to 'equilibrate' by moving into l
 ess populated areas. The macroscopic phenomenon of linear diffusion is gen
 erated by the microscopic phenomenon of random Brownian motion (the infini
 tesimal limit of short uncorrelated steps taken at small time intervals). 
 The latter is a commonly used model to represent uncertainty in particle m
 otion. However\, much more complicated processes occur in many important a
 pplications\, such as diffusion of a non-infinitesimal non-local nature\, 
 where the motion at a given point in space is influenced by events at many
  different scales.  Such processes arise in many different contexts\, for 
 example in continuum mechanics when surface diffusion is influenced by spa
 tial considerations (semipermeable membranes\, the quasigeostrophic equati
 on for atmospheric and oceanic flows) and in problems involving phase tran
 sitions. On a probabilistic level non-infinitesimal diffusions are often d
 escribed by Levy-type jump processes (a significant generalisation of Brow
 nian motion).\n\nWe shall discuss some important nonlinear partial differe
 ntial problems involving such diffusion processes. 
LOCATION:Room 3\, Mill Lane Lecture Rooms\, 8 Mill Lane\, Cambridge
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