Electron. J. Diff. Equ., Vol. 2015 (2015), No. 237, pp. 1-13.

Riemann problem for a two-dimensional quasilinear hyperbolic system

Chun Shen

This article concerns the study of the Riemann problem for a two-dimensional non-strictly hyperbolic system of conservation laws. The initial data are three constant states separated by three lines and are chosen so that one of the three interfaces of the initial data projects a planar delta shock wave. Based on the generalized characteristic analysis, the global solutions are constructed completely. The solutions reveal a variety of geometric structures for the interactions of delta shock waves with rarefaction waves, shock waves and contact discontinuities.

Submitted April 28, 2013. Published September 15, 2015.
Math Subject Classifications: 35L65, 35L67, 76N15.
Key Words: Conservation laws; delta shock wave; Riemann problem; generalized characteristic analysis.

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Chun Shen
School of Mathematics and Statistics Science
Ludong University
Yantai, Shandong Province 264025, China
Phone +86 535 6697510. Fax +86 535 6681264
email: shenchun3641@sina.com

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