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Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms

Tong Yang Changjiang Zhu Huijiang Zhao

Analysis of PDEs mathscidoc:1912.43972

Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 127, (6), 1311-1324, 1997
In this paper we prove an existence theorem of global smooth solutions for the Cauchy problem of a class of quasilinear hyperbolic systems with nonlinear dissipative terms under the assumption that only the <i>C</i><sup>0</sup>-norm of the initial data is sufficiently small, while the <i>C</i><sup>1</sup>-norm of the initial data can be large. The analysis is based on <i>a priori</i> estimates, which are obtained by a generalised Lax transformation.
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@inproceedings{tong1997global,
  title={Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms},
  author={Tong Yang, Changjiang Zhu, and Huijiang Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211006237708536},
  booktitle={Proceedings of the Royal Society of Edinburgh Section A: Mathematics},
  volume={127},
  number={6},
  pages={1311-1324},
  year={1997},
}
Tong Yang, Changjiang Zhu, and Huijiang Zhao. Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms. 1997. Vol. 127. In Proceedings of the Royal Society of Edinburgh Section A: Mathematics. pp.1311-1324. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211006237708536.
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