Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-16T20:37:51.354Z Has data issue: false hasContentIssue false
  • English
  • Français

Initial boundary value problems for isentropic gas dynamics

Published online by Cambridge University Press:  14 November 2011

Shigeharu Takeno
Shigeharu Takeno
Affiliation:
Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Ninocho-8050, Ikarashi, Niigata City, 950-21, Japan
Get access Rights & Permissions [Opens in a new window]

Synopsis

For piston problems for a system of isentropic gas dynamics, convergence theorems of a difference scheme are obtained by compensated compactness theory and by analysis of the difference scheme.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 1-2 , 1992 , pp. 1 - 23
Copyright
Copyright © Royal Society of Edinburgh 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Guiqiang, Chen. Convergence of the Lax–Friedrichs scheme for isentropic gas dynamics (III). Ada Math. Sci. 6 (1986), 75–120 (Chinese edition: 8 (1988), 101–134).Google Scholar
2Xiaxi, Ding, Guiqiang, Chen and Peizhu, Luo. Convergence of the Lax–Friedrichs scheme for isentropic gas dynamics (I)–(II). Ada Math. Sci. 5 (1985), 415–432, 433–472 (Chinese edition: 7 (1987), 467–481; 8 (1988), 61–94).Google Scholar
3Xiaxi, Ding, Guiqiang, Chen and Peizhu, Luo. A supplement to the papers Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (II)–(III). Ada Math. Sci. 9 (1989), 43–44.Google Scholar
4DiPerna, R. J.. Convergence of approximate solutions to conservation laws. Arch. Rational Mech. Anal. 82 (1983), 27–70.CrossRefGoogle Scholar
5DiPerna, R. J.. Convergence of the viscosity method for isentropic gas dynamics. Comm. Math. Phys. 91 (1983), 1–30.CrossRefGoogle Scholar
6Evans, L. C.. Weak convergence methods for nonlinear partial differential equations, CBMS regional conference series in mathematics 74 (Providence, R.I.: American Mathematical Society, 1990).CrossRefGoogle Scholar
7Lax, P. D.. Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math. 10 (1957), 537–566.CrossRefGoogle Scholar
8Liu, T. P.. Initial-boundary value problems for gas dynamics. Arch. Rational Mech. Anal. 64 (1977), 137–168.CrossRefGoogle Scholar
9Liu, T. P.. The free piston problem for gas dynamics. J. Differential Equations 30 (1978), 175–191.CrossRefGoogle Scholar
10Nishida, T.. Global solution for an initial boundary value problem of a quasilinear hyperbolic system. Proc. Japan Acad. 44 (1968), 642–646.Google Scholar
11Nishida, T. and Smoller, J.. Solutions in the large for some nonlinear hyperbolic conservation laws. Comm. Pure Appl. Math. 26 (1973), 183–200.CrossRefGoogle Scholar
12Nishida, T. and Smoller, J.. Mixed problems for nonlinear conservation laws. J. Differential Equations 23 (1977), 244–269.CrossRefGoogle Scholar
13Smoller, J.. Shock waves and reaction-diffusion equations (New York: Springer, 1982).Google Scholar
14Tartar, L.. Compensated compactness and applications to partial differential equations. In Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. 4, ed. Knops, R. J., Research Notes in Mathematics 39 (London: Pitman, 1979).Google Scholar