On a nonlocal model of non-isothermal phase separation

A nonlocal model of non-isothermal phase separation in binary alloys is presented. The model is deduced from a free energy with a nonconvex part taking into account nonlocal particle interaction. The model consists of a system of second order parabolic evolution equations for heat and mass, coupled by nonlinear drift terms and a state equation which involves a nonlocal interaction potential. The negative entropy turns out to be Lyapunov functional of the system and yields the key estimate for proving global existence and uniqueness results and for analyzing the asymptotic behaviour as time goes to infinity