Advertisement

“Simple” solutions of the equations of dynamics for a polytropic gas

  • L. V. Ovsyannikov
Article

Abstract

The notion of a “simple” solution of a system of differential equations that admit a local Lie group G of transformations of the basic space is considered as an invariant H-solution of type (0, 0) with respect to the subgroup HυG. Such solutions are attractive since they are described by explicit formulas that provide a clear physical interpretation for them. For gas-dynamic equations with a polytropic gas law, all simple solutions that are not related to special forms of gas flow are listed. Examples of simple solutions are given and the collapse phenomenon, which has been previously studied for barochronic flows, is described.

Keywords

Arbitrary Constant Simple Solution Factor System Isothermal Flow Typical Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. V. Ovsyannikov,Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).MATHGoogle Scholar
  2. 2.
    L. V. Ovsyannikov, “The SUBMODEL Program. Gas Dynamics,”Prikl. Mat. Mekh.,58, No. 4, 30–55 (1994).MATHMathSciNetGoogle Scholar
  3. 3.
    S. V. Golovin, “Optimal system of subalgebras for the Lie algebra of the operators admitted by the equations of gas dynamics for a polytropic gas,” Preprint No. 5-96, Institute of Hydrodynamics, Sib. Div., Russian Acad. of Sci., Novosibirsk (1996).Google Scholar
  4. 4.
    A. P. Chupakhin, “Barochronic gas flows,”Dokl. Ross. Akad. Nauk,352, No. 5, 624–626 (1997).MATHMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • L. V. Ovsyannikov

There are no affiliations available

Personalised recommendations