On the Smoluchowski-Kramers approximation for SPDEs and its interplay with large deviations and long time behavior

Sandra Cerrai; Mark Freidlin; Michael Salins

doi:10.3934/dcds.2017003

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2017, Volume 37, Issue 1: 33-76. Doi: 10.3934/dcds.2017003

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On the Smoluchowski-Kramers approximation for SPDEs and its interplay with large deviations and long time behavior

1.
University of Maryland, College Park, United States
2.
Boston University, Boston, United States

* Corresponding author
* Corresponding author

* Partially supported by the NSF grant DMS 1407615

Received: January 31, 2016

Revised: August 31, 2016

Published: September 2017

Partially supported by the NSF grant DMS 1407615

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Abstract

We discuss here the validity of the small mass limit (the so-called Smoluchowski-Kramers approximation) on a fixed time interval for a class of semi-linear stochastic wave equations, both in the case of the presence of a constant friction term and in the case of the presence of a constant magnetic field. We also consider the small mass limit in an infinite time interval and we see how the approximation is stable in terms of the invariant measure and of the large deviation estimates and the exit problem from a bounded domain of the space of square integrable functions.

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Mathematics Subject Classification: 60H15, 60F10, 35L71, 35K57, 49J45.

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