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

Smoluchowski-Kramers approximation in the case of variable friction