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Relaxation and diffusion enhanced dispersive waves

Shi Jin Courant Institute of Mathematical Sciences Jian-Guo Liu Temple University

Analysis of PDEs mathscidoc:1702.03074

Mathematical and Physical Sciences, 446, (1928), 555-563, 1994.9
The development of shocks in nonlinear hyperbolic conservation laws may be regularized through either diffusion or relaxation. However, we have observed surprisingly that for some physical problems, when both of the smoothing factors - diffusion and relaxation - coexist, under appropriate asymptotic assumptions, the dispersive waves are enhanced. This phenomenon is studied asymptotically in the sense of the Chapman-Enskog expansion and demonstrated numerically.
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@inproceedings{shi1994relaxation,
  title={Relaxation and diffusion enhanced dispersive waves},
  author={Shi Jin, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209140031129685409},
  booktitle={Mathematical and Physical Sciences},
  volume={446},
  number={1928},
  pages={555-563},
  year={1994},
}
Shi Jin, and Jian-Guo Liu. Relaxation and diffusion enhanced dispersive waves. 1994. Vol. 446. In Mathematical and Physical Sciences. pp.555-563. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209140031129685409.
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