Variational approach to constructing hyperbolic models of two-velocity media

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.