Uniform L_1 boundedness of solutions of hyperbolic conservation laws

Tai-Ping Liu Tong Yang

Analysis of PDEs mathscidoc:1912.43984

Methods and Applications of Analysis, 4, (3), 339-355, 1997.9
In this paper, we study the Li stability of perturbation of constant states for 2 x 2 systems of conservation laws. We introduce a nonlinear functional which is equivalent to the Li norm of the difference between the constant state and the approximate solutions consisting of elementary waves and is non-increasing in time for the limiting weak solution. This yields the Li stability of the constant states. The approximate solutions are constructed with the aid of wave tracing for the random choice method. Our functional reveals the aspects of nonlinear wave behavior, particularly the coupling of waves pertaining to different characteristic families, which affects the Li norm of the solutions.
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@inproceedings{tai-ping1997uniform,
  title={Uniform L_1 boundedness of solutions of hyperbolic conservation laws},
  author={Tai-Ping Liu, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211048576815548},
  booktitle={Methods and Applications of Analysis},
  volume={4},
  number={3},
  pages={339-355},
  year={1997},
}
Tai-Ping Liu, and Tong Yang. Uniform L_1 boundedness of solutions of hyperbolic conservation laws. 1997. Vol. 4. In Methods and Applications of Analysis. pp.339-355. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211048576815548.
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