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Relaxation and Diffusion Enhanced Dispersive Waves

Shi Jin and Jian-Guo Liu
Proceedings: Mathematical and Physical Sciences
Vol. 446, No. 1928 (Sep. 8, 1994), pp. 555-563
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52478
Page Count: 9
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Relaxation and Diffusion Enhanced Dispersive Waves
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Abstract

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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