Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock

In this paper, a four-quadrant Riemann problem for 2×2 system of hyperbolic conservation laws is considered in the case delta shock appearing at initial discontinuity. We also remove restriction that there only one planar wave each include existence two elementary waves discontinuity and classify 14 topologically distinct solutions. For case, we construct an analytic solution compute numerical solution.