Two-dimensional Riemann problem for a hyperbolic system of conservation laws in three pieces

This paper studies the two-dimensional Riemann problem for a hyperbolic system of conservation laws with three constant initial data separated by x-positive, y-positive and x-negative axes. Using the generalized characteristic analysis method, by considering the interactions of rarefaction waves, shock waves and contact discontinuities, 13 exact solutions and the corresponding criteria are obtained. Delta-shock waves appear in some solutions. Moreover, the numerical illustrations agree completely with the geometric structures of the exact solutions.