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Two-dimensional Riemann problems for zero-pressure gas dynamics with three constant states. (English) Zbl 1139.35073

Summary: The Riemann problems for two-dimensional zero-pressure gas dynamics are solved completely when the initial data take three constant states having discontinuities on \(x,y\)-positive and \(x\)-negative axes. With the help of characteristic analysis, by studying interactions among delta-shocks, vacuums and contact discontinuities, the Riemann solutions constructed exhibit nine different explicit configurations. The Mach-reflection-like configurations appear in some solutions.

MSC:

35L67 Shocks and singularities for hyperbolic equations
35L65 Hyperbolic conservation laws
76N15 Gas dynamics (general theory)
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