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We consider an interacting particle system with two species under strongcompetition dynamics between the two species. Then, through the hydrodynamiclimit procedure for the microscopic model, we derive a one-phase Stefan typefree boundary problem with non-linear diffusion, letting the competition ratedivergent. Non-linearity of diffusion comes from a zero-range dynamics for onespecies while we impose the other species to weakly diffuse according to theKawasaki dynamics for technical reasons, which macroscopically corresponds tothe vanishing viscosity method.

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