A dynamic inverse problem for a one-dimensional system of the Hopf-type equations is considered. A theorem on local solvability in the class of functions
analytic in the variable *x* is proved.

A one-dimensional system of the Hopf-type equations is considered. Axial solutions to problems in the field of modeling two-fluid interactions are sought. A nonlinear system of ordinary differential equations is obtained. Direct and inverse problems for the obtained ODE are considered. A theorem on local solvability is proven.

Two-velocity models of suspension hydrodynamics are considered, using the equality condition for chemical potentials of the phases or without this condition. The model equations are obtained by the conservation law method and are thermodynamically consistent under the assumption of one pressure or two pressure systems. Models are compared numerically on...

The paper considers applications of a two-velocity model of hydrody- namics for a two-phase medium for describing natural geological systems, such as movement of magma melts in magma channels, the flow of a river and the erosion of an unfixed sandy river bottom. The study deals with a test problem...

The paper considers a system of equations of motion of a two-phase medium with phase equilibrium in terms of pressure and temperature. The spectral analysis of the system was carried out for a one-dimensional case. Approximate numerical solutions of the Riemann problem about the decay of an arbitrary discontinuity were...

The paper studies the flow of a two-phase medium in a gravity field channel. The thermodynamically consistent equations of the mathematical model of the dynamics of a two-velocity medium with an admixture were developed within the framework of the method of conservation laws. Its numerical implementation was carried out based...

An initial boundary value problem for systems of viscous two-fluid media with equilibrium of pressure phases is considered. Using the test function method proposed by S.I. Pohozhaev and E. Mitidieri, the effect of boundary and initial conditions on the appearance, time and rate of destruction of solutions of this problem...

A system of the Burgers equations of the two-velocity hydrodynamics is obtained. We consider the Cauchy problem in the case of a one-dimensional system. The estimate of the stability of the solution is obtained. We have obtained a formula for the Cauchy problem for the one-dimensional system of equations that...

A series of the differential identities connecting velocities, pressure and body force in the two-velocity hydrodynamics equations with equilibrium of pressure phases are found. Some of these identities have a divergent form and can be considered to be certain conservation laws. It is detected that the flow functions for the...

A flow of incompressible viscous two-velocity fluids for the case of pressure equilibrium of phases at constant saturation of substances is described with the help of scalar functions. A system of differential equations for these functions is obtained. An example illustrating this method is presented.