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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Formation and propagation of singularities for $2\times 2$ quasilinear hyperbolic systems


Author: De-xing Kong
Journal: Trans. Amer. Math. Soc. 354 (2002), 3155-3179
MSC (2000): Primary 35L45, 35L67; Secondary 35L65, 76L05
Published electronically: April 2, 2002
MathSciNet review: 1897395
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Abstract: Employing the method of characteristic coordinates and the singularity theory of smooth mappings, in this paper we analyze the long-term behaviour of smooth solutions of general $2\times 2$ quasilinear hyperbolic systems, provide a complete description of the solution close to blow-up points, and investigate the formation and propagation of singularities for $2\times 2$ systems of hyperbolic conservation laws.


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Additional Information

De-xing Kong
Affiliation: Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai 200030, China
Email: dkong@mail.sjtu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02982-3
PII: S 0002-9947(02)02982-3
Keywords: Quasilinear hyperbolic system, smooth solution, blow-up of cusp type, shock, weak discontinuity
Received by editor(s): May 24, 2000
Received by editor(s) in revised form: May 4, 2001
Published electronically: April 2, 2002
Additional Notes: The author was supported in part by the National Science Foundation of China under Grant # 10001024 and the Special Funds for Major State Basic Research Projects of China.
Article copyright: © Copyright 2002 American Mathematical Society