Nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws
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- by Hailiang Liu and Jinghua Wang PDF
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Abstract:
This paper is to study the asymptotic stability of stationary discrete shocks for the Lax-Friedrichs scheme approximating nonconvex scalar conservation laws, provided that the summations of the initial perturbations equal to zero. The result is proved by using a weighted energy method based on the nonconvexity. Moreover, the $l^1$ stability is also obtained. The key points of our proofs are to choose a suitable weight function.References
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Additional Information
- Hailiang Liu
- Affiliation: Department of Mathematics, Henan Normal University, Xinxiang 453002, P. R. China
- Email: guozm@sun.ihep.ac.cn
- Jinghua Wang
- Affiliation: Institute of Systems Science, Academia Sinica, Beijing 100080, P.R.China
- Email: jwang@iss06.iss.ac.cn
- Received by editor(s): January 11, 1995
- Additional Notes: The first author was supported in part by the Science Foundation of Education of Commission of Henan Province and by the Institute of Mathematics, Academia Sinica
The second author was supported in part by the National Natural Science Foundation of China and by The Raymond and Beverly Sackler Institute of Scientific Computation - © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 1137-1153
- MSC (1991): Primary 39A11; Secondary 35L65
- DOI: https://doi.org/10.1090/S0025-5718-96-00733-8
- MathSciNet review: 1344617