Small mass asymptotic for the motion with vanishing friction

Details Small mass asymptotic for the motion with vanishing friction Small mass asymptotic for the motion with vanishing friction

2012-01-05

arxiv.org/abs/1201.1242v1

Mathematics

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Scientific paper

We consider the small mass asymptotic (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The friction coefficient is assumed to be vanishing within certain region. We introduce a regularization for this problem and study the limiting motion for the 1-dimensional case and a multidimensional model problem. The limiting motion is a Markov process on a projected space. We specify the generator and boundary condition of this limiting Markov process and prove the convergence.

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