82B26 Phase transitions (general)
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- phase transitions (2)
- Cahn-Hilliard type dynamics (1)
- Gibbs-Thomson law (1)
- Nonlinear and nonlocal evolution (1)
- Stefan problem (1)
- equations (1)
- existence (1)
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- C (2)
The Stefan problem is coupled with a spatially inhomogeneous and anisotropic Gibbs-Thomson condition at the phase boundary. We show the long-time existence of weak solutions for the non-degenerate Stefan problem with a
spatially inhomogeneous and anisotropic Gibbs-Thomson law and a conditional existence result for the corresponding degenerate Stefan problem. To this end, approximate solutions are constructed by means of variational problems
for energy functionals with spatially inhomogeneous and anisotropic interfacial energy. By passing to the limit, we establish solutions of the Stefan problem with a spatially inhomogeneous and anisotropic Gibbs--Thomson law in a weak generalized BV-formulation.