Abstract:
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.
Keywords:differential
partial equations of the first order, the method of additional
argument, the extended characteristic system.