On the hyperbolicity, stability and correctness of the cauchy problem for the system of equations of two-speed motion of two-phase media

Abstract

Unsteady one-dimensional two-speed flows of a disperse stream are investigated and properties of the respective system of differential equations are investigated. Propagation of small perturbations is studied on the example of a mixture of barotropic gas with incompressible particles. It is pointed out that the nonhyperbolicity and instability of small perturbations peculiar to the system of differential equations are due to incomplete definition of interaction between phases and inside the dispersed phase, and to transport effects, and unrelated to acoustic perturbation propagation. Estimates are obtained for the characteristic times of instability development in streams of the drop and bubble structure.