Smoluchowski-Kramers approximation in the case of variable friction
  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. 
Mark Freidlin, Wenqing Hu
math.PR math-ph math.MP