Nonlinear self-adjointness and conservation laws for some equation systems of two-phase media

The T B Anderson - R Jackson system of equations with the Stokes regime of wrapping around is considered, which describes in the isothermal case the dynamics of a mixture of gas and fine solid particles, taking into account the difference in velocities and the presence of the own particle phase pressure. The system includes the equations for the conservation of mass and momentum, written for each phase and supplemented by equations of state. The aim of the paper is the search of conservation laws for the system by means of N Kh Ibragimov's nonlinear self-adjointness method. For this purpose it was found a substitutions family, which corresponds to the nonlinear self-adjointness of equations of the T B Anderson - R Jackson system. Using this result and known symmetries of the equations system, the series of conservation laws were derived. It is noted that the analogous results are valid for the Kh A Rakhmatulin system of equations of a mixture dynamics with one pressure.