Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 184-207 |
| Number of pages | 24 |
| Journal | Journal of Mathematical Sciences |
| Volume | 179 |
| Issue number | 1 |
| DOIs | |
| State | Published - Nov 2011 |
| Externally published | Yes |
Bibliographical note
Funding Information:This work is supported in part by NSF Grants DMS-0803287 and DMS-0854982.