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Singularities of solutions for first order quasilinear hyperbolic systems

Published online by Cambridge University Press:  14 November 2011

Lee Da-tsin(Li Ta-tsien)  and
Shi Jia-hong
Lee Da-tsin(Li Ta-tsien)
Affiliation:
Department of Mathematics, Fudan University, Shanghai, China
Shi Jia-hong
Affiliation:
Department of Mathematics, Fudan University, Shanghai, China
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Synopsis

In this paper, the existence of global smooth solutions and the formation of singularities of solutions for strictly hyperbolic systems with general eigenvalues are discussed for the Cauchy problem with essentially periodic small initial data or nonperiodic initial data. A result of Klainerman and Majda is thus extended to the general case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 137 - 147
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

1Chao-hao, Gu. Shock-free global solutions for quasilinear hyperbolic systems. Selected works of the Math. Dept.of Fudan Univ. 1960, 36–39 (in Chinese).Google Scholar
2Lax, P. D.. Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Phys. 5 (1964), 611–613.CrossRefGoogle Scholar
3Jeffrey, A. and Donate, A.The occurrence of singularities in solutions of homogeneous systems of two first order quasilinear hyperbolic equations with smooth initial data. Wave Motion 1 (1979), 177–185.Google Scholar
4Da-tsin, Lee (Li Ta-tsien). Global regularity and formation of singularities of solutions to first order quasilinear hyperbolic systems. Proc. Roy. Soc. Edinburgh Sect. A 87 (1981), 255–261.Google Scholar
5Tie-hu, Qin. Global solutions for Cauchy problem of first order quasilinear equations. (To appear in Fudan Journal)Google Scholar
6.Klainerman, S. and Majda, A.. Formation of singularities of wave equations including the nonlinear vibrating string. Comm. Pure. Appl. Math. 33 (1980), 241–263.CrossRefGoogle Scholar