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.
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Dedicated to N. V. Krylov on the occasion of his 70th birthday
Translated from Problems in Mathematical Analysis 61, October 2011, pp. 155–174.
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Freidlin, M., Hu, W. Smoluchowski–Kramers approximation in the case of variable friction. J Math Sci 179, 184–207 (2011). https://doi.org/10.1007/s10958-011-0589-y
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DOI: https://doi.org/10.1007/s10958-011-0589-y