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UID:7074@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190405T110000
DTEND;TZID=Europe/Paris:20190405T120000
DTSTAMP:20241120T203413Z
URL:https://www.i2m.univ-amu.fr/evenements/quantitative-stochastic-homogen
 ization-and-regularity-theory-of-parabolic-equations-alexandre-bordas/
SUMMARY:Alexandre Bordas (I2M\, Aix-Marseille Université): Quantitative st
 ochastic homogenization and regularity theory of parabolic equations - Ale
 xandre Bordas
DESCRIPTION:Alexandre Bordas: We develop a quantitative theory of stochasti
 c homogenization for linear\, uniformly parabolic equations with coefficie
 nts depending on space and time. Inspired by recent works in the elliptic 
 setting\, our analysis is focused on certain subadditive quantities derive
 d from a variational interpretation of parabolic equations. These subaddit
 ive quantities are intimately connected to spatial averages of the fluxes 
 and gradients of solutions. We implement a renormalization-type scheme to 
 obtain an algebraic rate for their convergence\, which is essentially a qu
 antification of the weak convergence of the gradients and fluxes of soluti
 ons to their homogenized limits. As a consequence\, we obtain estimates of
  the homogenization error for the Cauchy-Dirichlet problem which are optim
 al in stochastic integrability. We also develop a higher regularity theory
  for solutions of the heterogeneous equation\, including a uniform C0\,1-t
 ype estimate and a Liouville theorem of every finite order.\nhttps://arxiv
 .org/abs/1705.07672\n\nVidéo : Des particules se déplaçant de manière 
 aléatoire dans un environnement aléatoire \n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Alexandre_Bordas.jpg
CATEGORIES:Séminaire,Probabilités
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