Asymptotic solutions of the Cahn-Hilliard system in the fast relaxation case

The paper deals with the construction and justification of asymptotic solutions to the Cahn-Hilliard system, which models the separation of phases in metastable equilibrium (crystallization processes). The authors construct an asymptotic solution that describes the dynamics of the interface, i.e., the surface where the phase transition occurs. It is shown that the solution obtained in the limit, as the small parameter tends to zero, satisfies a modified crystallization system with a generalized Gibbs-Thomson condition on the interface. Bibliography: 27 titles. Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 20, pp. 48–80, 1997.