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UID:1216@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160510T110000
DTEND;TZID=Europe/Paris:20160510T120000
DTSTAMP:20160425T090000Z
URL:https://www.i2m.univ-amu.fr/evenements/regularization-by-noise-for-tra
 nsport-and-kinetic-equations/
SUMMARY: (...): Regularization by noise for transport and kinetic equations
DESCRIPTION:: For some differential equations the addition of a carefully c
 hosen\, random noise term can produce a regularizing effect (e.g. solution
 s are more regular\, or restored uniqueness).I will first mention a few ea
 sy examples (ODEs) to introduce some of these regularizing mechanisms\, th
 en detail two cases where we have regularization for a PDE: the linear tra
 nsport equation and a kinetic equation with force term. I will present som
 e classical results for these two equations\, related to well-posedness an
 d regularity of solutions\, that in the stochastic setting can be obtained
  under weaker hypothesis. These results are based on a careful analysis of
  the stochastic characteristics and the regularising properties of some as
 sociated parabolic/elliptic PDE.I will conclude by introducing a new strat
 egy of proof based on stochastic exponentials and an associated parabolic 
 PDE\, which allows to obtain\, under even weaker hypothesis\, wellposednes
 s for stochastic PDEs in a class of solutions which are only regular in me
 an. This will be illustrated by an application to the transport equation. 
 http://www.proba.jussieu.fr/dw/doku.php?id=users:fedrizzi:index
CATEGORIES:Séminaire,Analyse Appliquée
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DTSTART:20160327T030000
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