### On a construction of the extended characteristic system for perfect gas of the elliptic type

#### S. N. Alekseenko1, T. A. Shemyakina2

Annotation In this paper the system of two quasilinear differential partial equations of the first order is investigated. Among other applications, it describes steady-stated non-vortex motion of the perfect gas at lack of friction and heat conduction in a neighborhood of a surface of passage from subsonic speeds to supersonic. The basic research technique is the method of additional argument. The considered system is reduced to the characteristic form when each equation contains derivatives only from one unknown function. For the system of equations in the characteristic form the extended characteristic system with additional argument is obtained. It is proved that at the special value of the additional argument a solution of the characteristic system gives a solution of the original equations. differential partial equations of the first order, the method of additional argument, the extended characteristic system.

1Professor of the mathematical analisis department, Arzamas state pedagogical institute, Arzamas; sn-alekseenko@yandex.ru.

2Associate professor of the higher mathematics Chair, St.-Petersburg State Polytechnic university, St.-Petersburg; sh_tat@mail.ru.

Citation: S. N. Alekseenko, T. A. Shemyakina, "[On a construction of the extended characteristic system for perfect gas of the elliptic type]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,11:2 (2009) 57–60 (In Russian)