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A model of a two-phase flow of compressible immiscible fluids is presented. Its derivation is based on the use of the theory of symmetric hyperbolic thermodynamically compatible systems. The model is an extension of the previously proposed thermodynamically compatible model of compressible two-phase flows due to the inclusion of new state variables of a medium associated with surface-tension forces. The governing equations of the model form a hyperbolic system of differential equations of the first order and satisfy the laws of thermodynamics (energy conservation and entropy increase). The properties of the model equations are studied, and it is shown that the Young–Laplace law of capillary pressure is fulfilled in the asymptotic approximation at the continuum level. [ABSTRACT FROM AUTHOR]

A mathematical model of a nonlinear elastic medium is considered. Discontinuous solutions of the model are studied numerically for the one-dimensional case. [ABSTRACT FROM AUTHOR]

We describe a method for representing the nonlinear system of gas dynamics equations in quasilinear form with symmetric coefficient matrices and, moreover, with a positive definite matrix at the time derivative. [ABSTRACT FROM AUTHOR]