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Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface. (English) Zbl 0723.73017
Among the results of M. E. Gurtin’s paper [see this Zbl 0723.73016] on the thermodynamics of two-phase rigid continua based on Gibbs’s notion of sharp phase-interface endowed with energy, entropy, and superficial force we remained those regarding the exact and approximate free boundary conditions at the interface and a hierarchy of free boundary problems. These problem are extremely difficult to solve because of nonlinearities inherent in the free boundary conditions. In the case of perfrect conductors, i.e. materials with infinite thermal conductivity, the temperature is constant and the corresponding free boundary problem reduces to a single set of evolution equations for interfaces.
The goal of this paper is the theory of rigid perfect conductors with interfaces that evolve as curves in \({\mathbb{R}}2\). The paper contains a lot of results of great interest regarding the evolution of an isothermal interface. To form an idea of the problems treated in this paper we present its main sections. I. The thermodynamics of evolving curves, II. Smooth interfacial motions, III. Interfacial motions with corners, and IV. Nonsmooth interfacial energies.

MSC:
74A15 Thermodynamics in solid mechanics
80A17 Thermodynamics of continua
35R35 Free boundary problems for PDEs
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