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Phase Boundaries in Alloys with Elastic Misfit

  • Harald Garcke
Part of the Progress in Mathematics book series (PM, volume 202)

Abstract

We study a mathematical model describing phase transformations in alloys with kinetics driven by mass transport and stress. To describe the dynamics, a Cahn-Hilliard system taking elastic effects into account is studied. Existence and uniqueness results for the resulting singular elliptic-parabolic system are given.

In the Cahn-Hilliard model, phase boundaries are described by a diffuse interface with small positive thickness. In the stationary case we identify the sharp interface free boundary problem that arises when the interfacial thickness tends to zero. In particular, we obtain a geometric partition problem generalizing variants of isoperimetric problems to situations where elastic interactions cannot be neglected.

Keywords

Free Boundary Phase Field Model Interfacial Thickness Elastic Effect Chemical Potential Difference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Harald Garcke
    • 1
  1. 1.Institut für Angewandte MathematikUniversität BonnBonnGermany

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