On a partially invariant solution of gas dynamics equations

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Abstract

The present paper is devoted to the study concerning partially invariant multidimensional solutions of gas dynamics equations, generalizing classical stationary two-dimensional gas flows. It is proved that the gas dynamics equations for such solutions reduce to a third-order dynamical system on a manifold. The singular manifolds of this system are investigated. The main attention is paid to the structure of invariant and non-invariant components of the solution, as well as the features of solutions near singular points. The existence of solutions conjugated through a shock wave, which correspond to the transition of integral curves from one sheet of the manifold to another, is proved.

About the authors

A. P. Chupakhin

Lavrentyev Institute of Hydrodynamics SB RAS; Novosibirsk State University

Email: chupakhin@hydro.nsc.ru
Novosibirsk, Russia; Novosibirsk, Russia

E. S. Stetsyak

Lavrentyev Institute of Hydrodynamics SB RAS; Novosibirsk State University

Email: stetsyak.e.s@hydro.nsc.ru
Novosibirsk, Russia; Novosibirsk, Russia

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