| Abstract: |
| I will discuss some recent results on two asymptotic problems for the Langevin equation with variable friction coefficient. The first is the small mass asymptotic behavior, known as the Smoluchowski-Kramers approximation, of the Langevin equation with strictly positive variable friction. The second result is about the limiting behavior of the solution when the friction vanishes in regions of the domain. The results generalize previous works due to Freidlin-Hu and Freidlin-Hu-Wentzell. My talk will be based on joint work with P. E. Souganidis (University of Chicago) and H. V. Tran (University of Wisconsin-Madison). |
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