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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Decay rate for perturbations of stationary discrete shocks for convex scalar
conservation laws


Authors: Hailiang Liu and Jinghua Wang
Journal: Math. Comp. 66 (1997), 69-84
MSC (1991): Primary 39A11; Secondary 35L65
MathSciNet review: 1377663
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Abstract: This paper is to study the decay rate for perturbations of stationary discrete shocks for the Lax-Friedrichs scheme approximating the scalar conservation laws by means of an elementary weighted energy method. If the summation of the initial perturbation over $(-\infty , j)$ is small and decays at the algebraic rate as $|j|\rightarrow \infty $, then the solution approaches the stationary discrete shock profiles at the corresponding rate as $n\rightarrow \infty $. This rate seems to be almost optimal compared with the rate in the continuous counterpart. Proofs are given by applying the weighted energy integration method to the integrated scheme of the original one. The selection of the time-dependent discrete weight function plays a crucial role in this procedure.


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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

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00804-1
PII: S 0025-5718(97)00804-1
Keywords: Decay rate, discrete shocks, Lax-Friedrichs scheme
Received by editor(s): May 19, 1995
Received by editor(s) in revised form: January 31, 1996
Additional Notes: The first author was supported in part by the National Natural Science Foundation of China 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 Texs Coordinating Board for Higher Education, Advanced Research Program.
Article copyright: © Copyright 1997 American Mathematical Society