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Global smooth solution of the nonisentropic gas dynamics system*

Published online by Cambridge University Press:  14 November 2011

Changjiang Zhu
Affiliation:
Wuhan Institute of Mathematical Sciences, The Chinese Academy of Sciences, P.O. Box 71007, Wuhan 430071, P.R. China

Abstract

In this paper, a sufficient condition (H) is given on initial values for which there is a unique smooth global in time solution of the initial value problem for a special nonisentropic gas dynamics system.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1996

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References

1Douglis, A.. Existence theorems for hyperbolic systems. Comm. Pure Appl. Math. 5 (1952), 119–54.CrossRefGoogle Scholar
2Hoff, D.. Global smooth solutions to quasilinear hyperbolic systems in diagonal form. J. Math. Anal. Appl. 86(1982), 221–38.CrossRefGoogle Scholar
3John, F.. Formation of singularities in one-dimensional nonlinear wave propagation. Comm. Pure Appl. Math. 27 (1974), 377405.CrossRefGoogle Scholar
4Johnson, J. L.. Global continuous solution of hyperbolic systems of quasilinear equations. Bull. Amer. Math. Soc. 73 (1967), 639–41.CrossRefGoogle Scholar
5Lax, P. D.. Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Phys. 5 (1964), 611–13.CrossRefGoogle Scholar
6Caizhong, Li and Jianhua, Wang. Globally smooth resolvability for non-diagonalizable quasilinear hyperbolic systems. Ada Math. Sci. 9 (1989), 297306.Google Scholar
7Ta-tsien, Li. Global regularity and formation of singularities of solutions to first order quasilinear hyperbolic systems. Proc. Roy. Soc. Edinburgh Sect. A 87 (1981), 255–61.Google Scholar
8Ta-tsien, Li and Wontzu, Yu. Cauchy's problems for quasilinear hyperbolic systems of the first order partial differential equation. Math. Progress Sinica 7 (1964), 152–71.Google Scholar
9Longwei, Lin. On the vacuum state for the equations of isentropic gas dynamics. J. Math. Anal. Appl. 121 (1987), 406–25.Google Scholar
10Liu, T. P.. Development of singularities in the nonlinear wave for quasilinear hyperbolic partial differential equations. J. Differential Equations 33 (1979), 92111.CrossRefGoogle Scholar
11Yongshu, Zheng. Global smooth solutions for systems of gas dynamics with dissipation. Ada Math. Sci. 7(1987), 383–90.Google Scholar
12Changjiang, Zhu, Caizhong, Li and Huijiang, Zhao. The existence of the global continuous solutions for a class of nonstrictly hyperbolic equations. Ada Math. Sci. 14 (1994), 96106 (in Chinese).Google Scholar