Small mass asymptotic for the motion with vanishing friction

Abstract

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.

final version for publication, accepted by Stochastic Processes and their Applications

References in corpus (1)

• Smoluchowski-Kramers approximation in the case of variable friction

Cited by in corpus (6)

• The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
• The Small-Mass Limit for Langevin Dynamics with Unbounded Coefficients and positive friction
• Wave front propagation for a reaction-diffusion equation in narrow random channels
• Wave propagation for reaction-diffusion equations on infinite random trees
• On the long-time behavior of a perturbed conservative system with degeneracy
• On the Langevin equation with variable friction