1201.1242 (Mark Freidlin et al.)

Small mass asymptotic for the motion with vanishing friction    [PDF]

Mark Freidlin, Wenqing Hu, Alexander Wentzell

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.

View original: http://arxiv.org/abs/1201.1242