We analyze a new class of one-dimensional interacting particle systems featuring random boundaries with a random motion that is coupled to the local particle density. We show that the hydrodynamic limiting behavior in these systems corresponds to the solution of an appropriate. Stefan (free-boundary) equation and describe some applications of these results.
"Hydrodynamic limits for one-dimensional particle systems with moving boundaries." Ann. Probab. 24 (2) 559 - 598, April 1996. https://doi.org/10.1214/aop/1039639355