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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
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