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

Author(s): De-xing Kong
Journal: Trans. Amer. Math. Soc. 354 (2002), 3155-3179.
MSC (2000): Primary 35L45, 35L67; Secondary 35L65, 76L05
Posted: April 2, 2002
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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: 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
Posted: 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.
Copyright of article: Copyright 2002, American Mathematical Society

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