An anisotropic, inhomogeneous, elastically modified Gibbs--Thomson law as singular limit of a diffuse interface model
- Garcke, Harald
- Kraus, Christiane
2010 Mathematics Subject Classification
- 49Q20, 35B25 82B26 58B20
- Van der Waals-Cahn-Hilliard energy, singular perturbations, anisotropic and inhomogeneous interfacial energy, elasticity, Gibbs-Thomson law
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.
- Adv. Math. Sci. Appl., 20 (2010) pp. 511--545.