Differentical equations, dynamical systems and optimal control

The classical solution of one overdetermined stationary system arising in two-velocity hydrodynamics

M. V. Urev^abc, Sh. Kh. Imomnazarov<sup>a

a</sup> ICM&MG SB RAS, 6, pr. Lavrent’eva, Novosibirsk, 630090, Russia
^b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
^c Siberian Institute of management-the branch of Ranepa, 6, Nizegorodskaya str., Novosibirsk, 630102, Russia

Abstract: The classical solution of an overdetermined stationary system of second order equations arising in a two-fluid medium is considered. Using the theory of potential and the Green's function for a given system, the existence of the classical solution in the case of specifying the Dirichlet boundary conditions is shown. The influence of the kinetic parameters of the medium on the solution of the system in question has been shown.

Keywords: Two- velocity hydrodynamics, viscous liquid, fundamental solution, potential of double layer, Green's function, the classical solution.

UDC: 517.946

MSC: 35A05

Received January 31, 2018, published December 14, 2018

DOI: 10.33048/semi.2018.15.134

Bibliographic databases:

•