L. Chayes et G. Swindle, HYDRODYNAMIC LIMITS FOR ONE-DIMENSIONAL PARTICLE-SYSTEMS WITH MOVING BOUNDARIES, Annals of probability, 24(2), 1996, pp. 559-598
We analyze a new class of one-dimensional interacting particle systems
featuring random boundaries with a random motion that is coupled to t
he local particle density. We show that the hydrodynamic limiting beha
vior in these systems corresponds to the solution of an appropriate St
efan (free-boundary) equation and describe some applications of these
results.