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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Formation and propagation of singularities for $2\times 2$ quasilinear hyperbolic systems
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by De-xing Kong PDF
Trans. Amer. Math. Soc. 354 (2002), 3155-3179 Request permission

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
  • 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.
  • © Copyright 2002 American Mathematical Society
  • 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
  • MathSciNet review: 1897395