a1 Department of Mechanical Engineering and Science and Advanced Research Institute of Fluid Science and Engineering, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan. email@example.com
a2 Dipartimento di Matematica, Università di Roma “La Sapienza", Piazzale A. Moro 2, 00185, Roma, Italy. firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity and prove that, under suitable smallness assumptions, the approach to equilibrium is where d is the dimension of the space, and C is a positive constant. This approach is not exponential, as typical in friction problems, and even slower than for the same problem with elastic collisions.
(Received March 31 2007)
(Revised October 16 2007)
(Online publication March 27 2008)
Mathematics Subject Classification: