Compactness Framework ofLpApproximate Solutions for Scalar Conservation Laws

Tong Yang Changjiang Zhu Huijiang Zhao

Analysis of PDEs mathscidoc:1912.431000

Journal of mathematical analysis and applications, 220, (1), 164-186, 1998.4
In this paper, we study the strong convergence of a sequence of uniform<i>L<sup>p</sup></i><sub>loc</sub>(<b>R</b><b>R</b><sup>+</sup>) bounded approximate solutions {<i>u</i><sup></sup>(<i>x</i>,<i>t</i>)} to the following scalar conservation laws[formula]with initial data[formula]Without the convexity assumption and growth condition at infinity for<i>f</i>(<i>x</i>,<i>t</i>,<i>u</i>), we prove strong convergence of a subsequence of {<i>u</i><sup></sup>(<i>x</i>,<i>t</i>)}. Under a more general growth condition than those in the previous work, we prove the existence of weak solution for the equation. The result obtained here generalizes those in earlier work. Some applications of the results are also given at the end of this paper.
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@inproceedings{tong1998compactness,
  title={Compactness Framework ofLpApproximate Solutions for Scalar Conservation Laws},
  author={Tong Yang, Changjiang Zhu, and Huijiang Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211138595787564},
  booktitle={Journal of mathematical analysis and applications},
  volume={220},
  number={1},
  pages={164-186},
  year={1998},
}
Tong Yang, Changjiang Zhu, and Huijiang Zhao. Compactness Framework ofLpApproximate Solutions for Scalar Conservation Laws. 1998. Vol. 220. In Journal of mathematical analysis and applications. pp.164-186. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211138595787564.
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