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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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$L_1$ stability for $2 \times 2$ systems of hyperbolic conservation laws
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by Tai-Ping Liu and Tong Yang PDF
J. Amer. Math. Soc. 12 (1999), 729-774 Request permission


In this paper, we study the evolution of the $L_1$ distance of solutions for systems of $2\times 2$ hyperbolic conservation laws. For the approximate solutions constructed by Glimm’s scheme with the aid of the wave tracing method, we introduce a nonlinear functional which is equivalent to the $L_1$ distance between solutions, nonincreasing in time, and expressed explicitly in terms of the wave patterns of the solutions. This functional reveals the nonlinear mechanism of wave interactions and coupling which affect the $L_1$ topology.
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Additional Information
  • Tai-Ping Liu
  • Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-2060
  • Email:
  • Tong Yang
  • Affiliation: Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
  • MR Author ID: 303932
  • Email:
  • Received by editor(s): March 8, 1998
  • Received by editor(s) in revised form: September 9, 1998
  • Published electronically: April 13, 1999
  • Additional Notes: The first author’s research was supported in part by NSF Grant DMS-9623025
    The second author’s research was supported in part by the RGC Competitive Earmarked Research Grant 9040290
  • © Copyright 1999 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 12 (1999), 729-774
  • MSC (1991): Primary 35L67, 76L05; Secondary 35L65, 35A05
  • DOI:
  • MathSciNet review: 1646841