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SUMMARY:Fractional diffusion limit of a linear kinetic transport equation 
 in a bounded domain - Pedro Aceves Sanchez\, Imperial College
DTSTART:20170605T141000Z
DTEND:20170605T151000Z
UID:TALK72705@talks.cam.ac.uk
CONTACT:Ariane Trescases
DESCRIPTION:In recent years\, the study of evolution equations featuring a
  fractional Laplacian has received many attention due the fact that they h
 ave been successfully applied into the modelling of a wide variety of phen
 omena\, ranging from biology\, physics to finance. The stochastic process 
 behind fractional operators is linked\, in the whole space\, to an $\\alph
 a$-stable processes as opposed to the Laplacian operator which is linked t
 o a Brownian stochastic process.\n\nIn addition\, evolution equations invo
 lving fractional Laplacians offer new interesting and very challenging mat
 hematical problems. There are several equivalent definitions of the fracti
 onal Laplacian in the whole domain\, however\, in a bounded domain there a
 re several options depending on the stochastic process considered.\n\nIn t
 his talk we shall present results on the rigorous passage from a velocity 
 jumping stochastic process in a bounded domain to a macroscopic evolution 
 equation featuring a fractional Laplace operator. More precisely\, we shal
 l consider the long-time/small mean-free path asymptotic behaviour of the 
 solutions of a re-scaled linear kinetic transport equation in a smooth bou
 nded domain.
LOCATION:CMS\, MR13
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