# Fourier Law, Phase Transitions and the Stationary Stefan Problem

@article{DeMasi2010FourierLP, title={Fourier Law, Phase Transitions and the Stationary Stefan Problem}, author={Anna De Masi and Errico Presutti and Dimitrios K. Tsagkarogiannis}, journal={Archive for Rational Mechanics and Analysis}, year={2010}, volume={201}, pages={681-725} }

We study the one-dimensional stationary solutions of the integro-differential equation which, as proved in Giacomin and Lebowitz (J Stat Phys 87:37–61, 1997; SIAM J Appl Math 58:1707–1729, 1998), describes the limit behavior of the Kawasaki dynamics in Ising systems with Kac potentials. 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…

## 22 Citations

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