This article is cited in 3 papers

Integration of the equations of gas dynamics for 2.5-dimensional solutions

M. A. Ignat'eva^a, A. P. Chupakhin<sup>b

a</sup> Novosibirsk State University
^b M. A. Lavrent'ev Institute of Hydrodynamics

Abstract: We integrate the equations of gas dynamics in finite form for the solutions in which the thermodynamic parameters depend only on one spatial variable. The corresponding motion of gas represents the nonlinear superposition of the one-dimensional gas motion corresponding to the invariant system and the two-dimensional motion determined by noninvariant functions. These motions are called 2.5-dimensional. We reduce the invariant system to a first-order implicit ordinary differential equation. We study various solutions of the latter. We construct some continuous and discontinuous solutions to the equations of gas dynamics and give their physical interpretation.

Keywords: partially invariant solutions, equations of gas dynamics, implicit differential equations.

UDC: 517.9+533

Received: 01.11.2005
Revised: 09.03.2006

 English version: Siberian Mathematical Journal, 2007, 48:1, 84–94

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