Interface dynamics and Stefan problem from a microscopic conservative model

Rendiconti di Matematica e delle Sue Applicazioni

B. Rüdiger¹  P. Buttಠ L. Bertini³ 

[1] Universitaet Bochum;Università dell’Aquila;Università di Roma La Sapienza;

关键词: field models;    stefan problem;    hydrodynamic limit;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown