A one-phase Stefan problem with non-linear diffusion from highly competing two-species particle systems

Abstract

We consider an interacting particle system with two species under strong competition dynamics between the two species. Then, through the hydrodynamic limit procedure for the microscopic model, we derive a one-phase Stefan type free boundary problem with nonlinear diffusion, letting the competition rate divergent. Non-linearity of diffusion comes from a zero-range dynamics for one species while we impose the other species to weakly diffuse according to the Kawasaki dynamics for technical reasons, which macroscopically corresponds to the vanishing viscosity method.