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V. G. Danilov, G. A. Omel’yanov and E. V. Radkevich, “Hugoniot-Type Conditions and Weak Solutions to the phase Field System,” European Journal of Applied Mathematics, Vol. 10, 1999, pp. 55-77.

has been cited by the following article:

• TITLE: Solidification and Structuresation of Instability Zones

  AUTHORS: Evgeniy Alexseevich Lukashov, Evgeniy Vladimirovich Radkevich

  KEYWORDS: Solidification, Structuresation of Instability Zones, Phase Field Model

  JOURNAL NAME: Applied Mathematics, Vol.1 No.3, September 29, 2010

  ABSTRACT: Two mathematical crystallization models describing structure formations in instability zones are proposed and justified. The first model, based on a phase field system, describes crystallization processes in binary alloys. The second model, based on a modified Biot model of a porous medium and the convective Cahn–Hilliard model, governs oriented crystallization. Physical interpretation and numerical analysis are discussed.