Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-02T21:51:28.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Large-time behaviour of solutions for the outer pressure problem of a viscous heat-conductive one-dimensional real gas

Published online by Cambridge University Press:  14 November 2011

L. Hsiao  and
T. Luo
L. Hsiao
Affiliation:
Academia Sinica, Institute of Mathematics, Beijing 100080, P.R. China
T. Luo
Affiliation:
Academia Sinica, Institute of Mathematics, Beijing 100080, P.R. China
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the large-time behaviour of solutions for the outer pressure problem of a viscous heat-conductive one-dimensional real gas. A conclusive answer to the problem of asymptotic behaviour is given in Theorem 1.2.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 6 , 1996 , pp. 1277 - 1296
Copyright
Copyright © Royal Society of Edinburgh 1996

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

1Becker, E.. Gasdynamic (Stuttgart: Teubner, 1966).Google Scholar
2Dafermos, C. M.. Global smooth solutions to the initial-boundary value problem for the equation of one-dimensional nonlinear thermoviscoelasticity. SIAM J. Math. Anal. 13 (1982), 397–408.CrossRefGoogle Scholar
3Dafermos, C. M. and Hsiao, L.. Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity. Nonlinear Anal. 6 (1982), 435–54.CrossRefGoogle Scholar
4Dafermos, C. M. and Hsiao, L.. Development of singularities in solutions of the equations of nonlinear thermoelasticity. Quart. Appl. Math. 44 (1986), 463–74.CrossRefGoogle Scholar
5Kawohl, B.. Global existence of large solutions to initial boundary value problems for a viscous, heat-conducting one-dimensional real gas. J. Differential Equations 58 (1985), 76–103.Google Scholar
6Kazhikhov, A. V. and Shelukhin, V. V.. Unique global solution with respect to time of initialboundary value problems for one-dimensional equations of a viscous gas. Prikl. Mat. Mekh. 41 (1977), 282–91; English translation: J. Appl. Math. Mech. 41 (1977), 273–82.Google Scholar
7Luo, T.. On the outer pressure problem of a viscous heat-conductive one-dimensional real gas (to appear).Google Scholar
8Nagasawa, T.. On the one-dimensional motion of the polytropic ideal gas no-fixed on the boundary. J. Differential Equations 65 (1986), 49–67.CrossRefGoogle Scholar
9Nagasawa, T.. On the outer pressure problem of the one-dimensional polytropic ideal gas. Japan J.Appl. Math. 5 (1988), 53–85.CrossRefGoogle Scholar
10Nagasawa, T.. Global asymptotics of the outer pressure problem with free boundary. Japan J. Appl. Math. 5 (1988), 205–24.CrossRefGoogle Scholar
11Slemrod, M.. Global existence, uniqueness and asymptotic stability of classical smooth solutions in one-dimensional, nonlinear thermoelasticity. Arch. Rational Mech. Anal. 76 (1981), 97–133.CrossRefGoogle Scholar
12Zel'dovich, Y. B. and Raizer, Y. P.. Physics of shock waves and high-temperature hydrodynamic phenomena, Vol. II (New York: Academic Press, 1967).Google Scholar