TY - JOUR
T1 - Interaction Of The Elementary Waves For Shallow Water Equations With Discontinuous Topography
AU - Zhang, Qinglong
AU - Sheng, Wancheng
AU - Zheng, Yuxi
N1 - Funding Information:
Acknowledgments. This work is partially supported by NSFC 11771274. The authors are very grateful to the anonymous referees for their corrections and suggestions, which improved the original manuscript greatly.
Publisher Copyright:
© 2021 International Press
PY - 2021
Y1 - 2021
N2 - The Riemann problem of one dimensional shallow water equations with discontinuous topography has been constructed recently. The elementary waves include shock waves, rarefaction waves, and the stationary wave. The stationary wave appears when the water depth changes, especially when there exists a bottom step. In this paper, we are mainly concerned with the interaction between a stationary wave with either a shock wave or a rarefaction wave. By using the characteristic analysis methods, the evolution of waves is described during the interaction process. The solution in large time scale is also presented in each case. The results may contribute to research on more complicated wave interaction problems.
AB - The Riemann problem of one dimensional shallow water equations with discontinuous topography has been constructed recently. The elementary waves include shock waves, rarefaction waves, and the stationary wave. The stationary wave appears when the water depth changes, especially when there exists a bottom step. In this paper, we are mainly concerned with the interaction between a stationary wave with either a shock wave or a rarefaction wave. By using the characteristic analysis methods, the evolution of waves is described during the interaction process. The solution in large time scale is also presented in each case. The results may contribute to research on more complicated wave interaction problems.
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U2 - 10.4310/CMS.2021.v19.n5.a9
DO - 10.4310/CMS.2021.v19.n5.a9
M3 - Article
AN - SCOPUS:85120935959
SN - 1539-6746
VL - 19
SP - 1381
EP - 1402
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 5
ER -