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Uniform Cooling of Alloys

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Abstract.

A phase separation process model formed by the Cahn– Hilliard equation and the heat equation is considered. The mobility coefficient in the Cahn–Hilliard equation is assumed to be an increasing function of the temperature. This property is of importance at the latest stage of the cooling process. The existence and uniqueness of a weak solution is proved, and a uniform cooling problem is studied. Obtained results can be used to control the cooling process and to create alloys with a uniform structure.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade da Beira Interior, Rua Marquês D'Àvila e Bolama, 6200, Covilhâ, Portugal

    Paulo Rebelo

  2. Centro de Matemática da Universidade do Porto, Departamento de Matemática Aplicada, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal

    Georgi V. Smirnov

Authors
  1. Paulo Rebelo
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  2. Georgi V. Smirnov
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Correspondence to Paulo Rebelo or Georgi V. Smirnov.

Additional information

2000 Mathematics Subject Classification. 35K30, 35Q99, 49J20.

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Rebelo, P., Smirnov, G. Uniform Cooling of Alloys. J Dyn Control Syst 11, 413–432 (2005). https://doi.org/10.1007/s10883-005-6588-x

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  • DOI: https://doi.org/10.1007/s10883-005-6588-x

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