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**On the two-phase Stefan problem with interfacial energy and entropy.**
*(English)*
Zbl 0654.73008

Starting from general thermodynamical laws which are appropriate to a continuum and which include interfacial contributions for both energy and entropy, the author develops a theoretical framework which can afford the description of phenomena such as supercooling in which a liquid supports temperatures below its freezing point, or superheating, the analogous phenomenon for solids, or dendrite formation in which simple shapes, such as spheres, evolve to complicated tree-like structures. The equilibrium theory under isothermal boundary is discussed by defining the stable states as minimizers of a global free-energy. Also, a quasi-static model for situations in which the interface moves slowly compared with the time scale for heat conclusion is introduced. Global growth-conditions are established.

Reviewer: D.Polisevski

### MSC:

74A15 | Thermodynamics in solid mechanics |

76T99 | Multiphase and multicomponent flows |

35R35 | Free boundary problems for PDEs |

76A99 | Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena |

74Axx | Generalities, axiomatics, foundations of continuum mechanics of solids |

### Keywords:

equilibrium stability; interfacial instabilities; capillarity relation; quasi-linear theory; dentritic growth; solidification; supercooling; freezing point; superheating; equilibrium theory; isothermal boundary; stable states; global free-energy; quasi-static model; Global growth- conditions
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\textit{M. E. Gurtin}, Arch. Ration. Mech. Anal. 96, 199--241 (1986; Zbl 0654.73008)

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### References:

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