傅立叶定律、相变和定态Stefan问题
Fourier law, phase transitions and the stationary Stefan problem
摘要：
本文研究了由Giacomin和Lebowitz从Kawasaki动力学导出的具有Kac势的Ising系统\cite{GiacominLebowitz}中的积分微分方程的一维定态解.我们构建固定的解决方案与非零电流和证明的傅立叶定律的热力学极限的有效性表明，低于临界温度的极限平衡剖面具有不连续性（定义的接口的位置），并满足一个固定的自由边界Stefan问题。过冷和过热的影响也进行了研究。我们表明，如果亚稳态值施加在边界处，那么介观固定配置文件不再是单调的，因此傅立叶定律是不满意的。然而，它在热力学极限中恢复其有效性，其中极限轮廓再次远离界面单调。
英文摘要：
We study the one-dimensional stationary solutions of an integro-differential equation derived by Giacomin and Lebowitz from Kawasaki dynamics in Ising systems with Kac potentials, \cite{GiacominLebowitz}. We construct stationary solutions with non zero current and prove the validity of the Fourier law in the thermodynamic limit showing that below the critical temperature the limit equilibrium profile has a discontinuity (which defines the position of the interface) and satisfies a stationary free boundary Stefan problem. Under-cooling and over-heating effects are also studied. We show that if metastable values are imposed at the boundaries then the mesoscopic stationary profile is no longer monotone and therefore the Fourier law is not satisfied. It regains however its validity in the thermodynamic limit where the limit profile is again monotone away from the interface.
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