Formation and propagation of singularities for quasilinear hyperbolic systems

Author:
De-xing Kong

Journal:
Trans. Amer. Math. Soc. **354** (2002), 3155-3179

MSC (2000):
Primary 35L45, 35L67; Secondary 35L65, 76L05

DOI:
https://doi.org/10.1090/S0002-9947-02-02982-3

Published electronically:
April 2, 2002

MathSciNet review:
1897395

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Abstract | References | Similar Articles | Additional Information

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 quasilinear hyperbolic systems, provide a complete description of the solution close to blow-up points, and investigate the formation and propagation of singularities for 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:
https://doi.org/10.1090/S0002-9947-02-02982-3

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