Interface dynamics and Stefan problem from a microscopic conservative model
Lorenzo Bertini, Paolo Buttà, Barbara Rüdiger · DOAJ (DOAJ: Directory of Open Access Journals) · 1999
We consider a stochastic spin system coupled to a linear diffusion process. The coupling is such that there is a locally conserved quantity. The equilibrium states are the corresponding canonical Gibbs measures. We prove that, under a diffusive scaling limit, the macroscopic density of the conserved quantity solves a non–linear diffusion equation. For certain values of the parameters a phase transition occurs; in this case the macroscopic equation degenerates and is the weak formulation of the two phases Stefan problem.