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Properties of the Wave Curves in the Shallow Water Equations with Discontinuous Topography

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Abstract

We first establish the monotonicity of the curves of composite waves for shallow water equations with discontinuous topography. Second, a critical investigation of the Riemann problem yields deterministic results for large data on the existence of Riemann solutions made of Lax shocks, rarefaction waves, and admissible stationary contacts. Although multiple solutions can be constructed for certain Riemann data, we can determine relatively large neighborhoods of Riemann data in which the Riemann problem admits a unique solution.

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Authors and Affiliations

  1. Department of Mathematics, International University, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam

    Mai Duc Thanh

  2. Nguyen Huu Cau High School, 07 Nguyen Anh Thu, Trung Chanh, Hoc Mon, Ho Chi Minh City, Vietnam

    Dao Huy Cuong

Authors
  1. Mai Duc Thanh
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  2. Dao Huy Cuong
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Correspondence to Mai Duc Thanh.

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Communicated by Ahmad Izani MD. Ismail.

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Thanh, M.D., Cuong, D.H. Properties of the Wave Curves in the Shallow Water Equations with Discontinuous Topography. Bull. Malays. Math. Sci. Soc. 39, 305–337 (2016). https://doi.org/10.1007/s40840-015-0186-1

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  • DOI: https://doi.org/10.1007/s40840-015-0186-1

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