The application of the differential-constraints method to the two-dimensional equations of gas dynanics

• Published in: Journal of applied mathematics and mechanics 1999, Vol.63 (6), p.885-891
• Main Authors: Meleshko, S.V., Shapeev, V.P.
• Format: Article
• Language: English
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/S0021-8928(00)00006-X

The differential-constraints (DC) method is used to distinguish and construct individual classes of solutions of the two-dimensional equations of gas dynamics with plane and axial symmetry. The solutions (the DP-solutions), which satisfy one, two and three first-order differential constraints are classified. The solution of the Cauchy problem with data on the line of common position in these cases has three, two and one arbitrary functions respectively. In the case of solutions with three- and two-function arbitrariness all the differential constraints compatible with the system considered are indicated. The individual DP-solutions of the gas-dynamics equations are constructed using them. In the case of single-function arbitrariness the differential constraints compatible with the gas-dynamics equations are obtained. This class of solutions includes the well-known generalized Prandtl-Meyer waves. The construction of the DP-solutions of this class reduces to the integration of a system of ordinary differential equations, which is a new representation of this class of solutions.