Communications in Mathematical Sciences
Volume 19 (2021)
Interaction of the elementary waves for shallow water equations with discontinuous topography
Pages: 1381 – 1402
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.
shallow water equations, source term, interaction of elementary waves, Riemann problem
2010 Mathematics Subject Classification
Primary 35L60, 35L65, 35L80, 35R35. Secondary 35L50.
This work is partially supported by NSFC 11771274.
Received 24 May 2020
Accepted 6 January 2021
Published 11 November 2021