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Nonlinear Stability of Stationary Discrete Shocks for Nonconvex Scalar Conservation Laws

Authors: Hailiang Liu and Jinghua Wang
Journal: Math. Comp. 65 (1996), 1137-1153
MSC (1991): Primary 39A11; Secondary 35L65
MathSciNet review: 1344617
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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.

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Additional Information

Hailiang Liu
Affiliation: Department of Mathematics, Henan Normal University, Xinxiang 453002, P. R. China

Jinghua Wang
Affiliation: Institute of Systems Science, Academia Sinica, Beijing 100080, P.R.China

Keywords: Stability, discrete shocks, Lax-Friedrichs scheme
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
Article copyright: © Copyright 1996 American Mathematical Society

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