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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

BV estimates of Lax-Friedrichs' scheme for a class of nonlinear hyperbolic conservation laws


Authors: Tong Yang, Huijiang Zhao and Changjiang Zhu
Journal: Proc. Amer. Math. Soc. 131 (2003), 1257-1266
MSC (1991): Primary 35L60, 35L65, 65N12
Published electronically: October 1, 2002
MathSciNet review: 1948118
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Abstract: We give uniform BV estimates and $L^1$-stability of Lax-Friedrichs' scheme for a class of $n\times n$ systems of strictly hyperbolic conservation laws whose integral curves of the eigenvector fields are straight lines, i.e., Temple class, under the assumption of small total variation. This implies that the approximate solutions generated via the Lax-Friedrichs' scheme converge to the solution given by the method of vanishing viscosity or the Godunov scheme, and then the Glimm scheme or the wave front tracking method.


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Additional Information

Tong Yang
Affiliation: Department of Mathematics, City University of Hong Kong, Hong Kong
Email: matyang@math.cityu.edu.hk

Huijiang Zhao
Affiliation: Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan, People’s Republic of China
Email: hjzhao@wipm.ac.cn

Changjiang Zhu
Affiliation: Laboratory of Nonlinear Analysis and Department of Mathematics, Central China Normal University, Wuhan, People’s Republic of China
Email: cjzhu@ccnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06688-1
PII: S 0002-9939(02)06688-1
Keywords: Hyperbolic systems of conservation laws, Lax-Friedrichs' scheme, BV estimates
Received by editor(s): December 5, 2001
Published electronically: October 1, 2002
Additional Notes: The first author was supported in part by the Research Grants Council of the Hong Kong Special Administrative Region, China (CityU 1032/98P)
The second author was supported in part by a grant from the National Natural Science Foundation of China (The Youth Foundation) and a grant from the Chinese Academy of Sciences entitled “Yin Jin Guo Wai Jie Chu Ren Cai Ji Jing".
The third author was supported in part by a grant from the National Natural Science Foundation of China $#$10171037 and two grants from the Ministry of Education of China entitled “Liu Xue Hui Guo Ren Yuan Ji Jing" and “Gao Deng Xue Xiao Zhong Dian Shi Yang Shi Ji Jing", respectively.
Communicated by: Suncica Canic
Article copyright: © Copyright 2002 American Mathematical Society