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Variational approach to constructing hyperbolic models of two-velocity media

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

A generalized Hamilton variational principle of the mechanics of two-velocity media is proposed, and equations of motion for homogeneous and heterogeneous two-velocity continua are formulated. It is proved that the convexity of internal energy ensures the hyperbolicity of the one-dimensional equations of motion of such media linearized for the state of rest. In this case, the internal energy is a function of both the phase densities and the modulus of the difference in velocity between the phases. For heterogeneous media with incompressible components, it is shown that, in the case of low volumetric concentrations, the dependence of the internal energy on the modulus of relative velocity ensures the hyperbolicity of the equations of motion for any relative velocity of motion of the phases.

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Authors and Affiliations

  1. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, 630090, Novosibirsk

    S. L. Gavrilyuk

  2. Joint Institute of Geology, Geophysics, and Mineralogy, Siberian Division, Russian Academy of Sciences, 630090, Novosibirsk

    Yu. V. Perepechko

Authors
  1. S. L. Gavrilyuk
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  2. Yu. V. Perepechko
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the present location of work: Universite of Aix-Marseille III, Marseille 13397

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 39–54, September–October, 1998.

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Gavrilyuk, S.L., Perepechko, Y.V. Variational approach to constructing hyperbolic models of two-velocity media. J Appl Mech Tech Phys 39, 684–698 (1998). https://doi.org/10.1007/BF02468039

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  • DOI: https://doi.org/10.1007/BF02468039

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