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The entropy principle for interfaces. Fluids and solids. (English) Zbl 1194.35003

This paper is a systematic theory for interfaces of fluids and solids, based on the entropy principle of rational thermodynamics. The approach differs substantially from existing presentations of interface problems and provides several new aspects. Balance laws for mass, momentum, energy, and entropy are formulated as distributional equations, in this version they attain their natural form. In addition, the author gives a systematic study of frame indifference, and he shows how this implies important structural properties of interfacial terms. Finally, some theorems on the necessity of entropy inequalities are given. Properties of classical equilibrium thermodynamics and existing non-equilibrium thermodynamics are contained in the theory presented here. According to the author the content of this paper will be completed by another one, where more examples of interfacial problems, in particular those with surface tension, will be treated.

MSC:

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35K40 Second-order parabolic systems
35Q35 PDEs in connection with fluid mechanics
46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
74A15 Thermodynamics in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
76A02 Foundations of fluid mechanics
80A17 Thermodynamics of continua
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