WIAS Preprint No. 1467, (2009)

An anisotropic, inhomogeneous, elastically modified Gibbs--Thomson law as singular limit of a diffuse interface model



Authors

  • Garcke, Harald
  • Kraus, Christiane

2010 Mathematics Subject Classification

  • 49Q20, 35B25 82B26 58B20

Keywords

  • Van der Waals-Cahn-Hilliard energy, singular perturbations, anisotropic and inhomogeneous interfacial energy, elasticity, Gibbs-Thomson law

Abstract

We consider the sharp interface limit of a diffuse phase field model with prescribed total mass taking into account a spatially inhomogeneous anisotropic interfacial energy and an elastic energy. The main aim is the derivation of a weak formulation of an anisotropic, inhomogeneous, elastically modified Gibbs-Thomson law in the sharp interface limit. To this end we show that one can pass to the limit in the weak formulation of the Euler-Lagrange equation of the diffuse phase field energy.

Appeared in

  • Adv. Math. Sci. Appl., 20 (2010) pp. 511--545.

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