On the Forced Motion of a Heavy Particle in a Random Medium I. Existence of Dynamics

V. Sidoravicius, L. Triolo, M.E. Vares

1998, v.4, Issue 4, 629-647


We consider the one-dimensional mechanical system, consisting of a heavy particle of mass $M$, subject to a constant positive force $F$ and to elastic collisions with infinitely many neutral particles of mass $m$, $M\geq m$. Initially all particles are standing. We prove that the corresponding dynamics is well defined almost everywhere with respect to the initial measure, provided that the initial distributions of interparticle distances are i.i.d. and their common distribution is absolutely continuous with respect to the Lebesgue measure.

Keywords: mechanical system,multiple collision


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