WIAS Preprint No. 656, (2001)

On a nonlocal phase separation model


  • Gajewski, Herbert
  • Zacharias, Klaus

2010 Mathematics Subject Classification

  • 35K45 35K57 35B40 80A22 92C15 92D25


  • Cahn-Hilliard equation, initial boundary value problem, reaction-diffusion equations, a priori estimates, Lyapunov function, equilibria, asymptotic behaviour, classical thermodynamics, phase changes, chemotaxis


An alternative to the Cahn-Hilliard model of phase separation for two-phase systems in a simplified isothermal case is given. It introduces nonlocal terms and allows reasonable bounds for the concentrations. Using the free energy as Lyapunov functional the asymptotic state of the system is investigated and characterized by a variational principle.

Appeared in

  • J. Math. Anal. Appl., 286 (2003) pp. 11--31.

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