Smoluchowski-Kramers approximation in the case of variable friction

M. Freidlin, W. Hu

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We consider the small mass asymptotics (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The limit of the solution in the classical sense does not exist in this case. We study a modification of the Smoluchowski-Kramers approximation. Some applications of the Smoluchowski-Kramers approximation to problems with fast oscillating or discontinuous coefficients are considered. Bibliography: 15 titles.

Original languageEnglish (US)
Pages (from-to)184-207
Number of pages24
JournalJournal of Mathematical Sciences
Issue number1
StatePublished - Nov 2011
Externally publishedYes

Bibliographical note

Funding Information:
This work is supported in part by NSF Grants DMS-0803287 and DMS-0854982.


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