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SUMMARY:Large time behavior of infinite dimensional systems under the Smol
 uchowski-Kramers approximation - Sandra Cerrai (University of Maryland\, C
 ollege Park\; University of Maryland\, College Park)
DTSTART:20181130T110000Z
DTEND:20181130T123000Z
UID:TALK115492@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:I will discuss the validity of the so-called Smoluchowski-Kram
 ers approximation for systems with an infinite number of degrees of freedo
 m in a finite time. Then\, I will investigate the validity of such approxi
 mation for large time. In particular\, I will address the problem of the c
 onvergence\, in the small mass limit\, of statistically invariant states f
 or a class of semi-linear damped wave equations\, perturbed by an additive
  Gaussian noise\, with quite general nonlinearities. More precisely\, I wi
 ll show how the first marginals of any sequence of invariant measures for 
 the stochastic wave equation converge in a suitable Wasserstein metric to 
 the unique invariant measure of the limiting stochastic semi-linear parabo
 lic equation obtained in the Smoluchowski-Kramers approximation.
LOCATION:Seminar Room 2\, Newton Institute
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