L1-stability of stationary discrete shocks

Jian-Guo Liu New York University Zhouping Xin New York University

Analysis of PDEs mathscidoc:1702.03077

Mathematics of Computation, 60, (201), 233-244, 1993.1
The nonlinear stability in the {L^p} -norm, p ≥ 1 , of stationary weak discrete shocks for the Lax-Friedrichs scheme approximating general m × m systems of nonlinear hyperbolic conservation laws is proved, provided that the summations of the initial perturbations equal zero. The result is proved by using both a weighted estimate and characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the Lax-Friedrichs scheme.
Lax-Friedrichs scheme, hyperbolic systems of conservation laws, discrete shock profiles, nonlinear stability
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@inproceedings{jian-guo1993l1-stability,
  title={L1-stability of stationary discrete shocks},
  author={Jian-Guo Liu, and Zhouping Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209142943795906413},
  booktitle={Mathematics of Computation},
  volume={60},
  number={201},
  pages={233-244},
  year={1993},
}
Jian-Guo Liu, and Zhouping Xin. L1-stability of stationary discrete shocks. 1993. Vol. 60. In Mathematics of Computation. pp.233-244. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209142943795906413.
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