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

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... with rarefaction waves, shock waves and contact discontinuities.