Riemann problem for a geometrical optics system

The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics, in which the flux contains the nonconvex function possessing an infinite number of inflection points. Firstly, the generalized Rankine-Hugoniot relations and entropy condition of delta shock waves and left(right)-contact delta shock waves are proposed and clarified. Secondly, with the help of the convex hull, seven kinds of structures of Riemann solutions are obtained. The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities, vacuums and delta shock waves. Finally, numerical experiments confirm the theoretical analysis.