WIAS Preprint No. 671, (2001)

On a nonlocal model of non-isothermal phase separation


  • Gajewski, Herbert

2010 Mathematics Subject Classification

  • 35K45 35K57 35B40 80A20 80A22


  • Coupled Cahn-Hilliard equations, binary alloys, segregation model, nonlocal interaction, free energy, entropy, Onsager relations, initial boundary value problem, global existence and uniqueness, Lyapunov function, asymptotic behaviour


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.

Appeared in

  • Adv. Math. Sci. Appl., 12 (2002) pp. 569--586.

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