$L_1$ stability for $2 \times 2$ systems of hyperbolic conservation laws
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- by Tai-Ping Liu and Tong Yang
- J. Amer. Math. Soc. 12 (1999), 729-774
- DOI: https://doi.org/10.1090/S0894-0347-99-00292-1
- Published electronically: April 13, 1999
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Abstract:
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.References
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Bibliographic Information
- Tai-Ping Liu
- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-2060
- Email: liu@math.stanford.edu
- Tong Yang
- Affiliation: Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
- MR Author ID: 303932
- Email: matyang@cityu.edu.hk
- 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: https://doi.org/10.1090/S0894-0347-99-00292-1
- MathSciNet review: 1646841