Two-Dimensional Riemann Problem for a Hyperbolic System of Nonlinear Conservation Laws : I. Four-J Cases

The Riemann problem for a two-dimensional 2 × 2 hyperbolic system of nonlinear conservation laws has been. solved analytically. The solutions reveal a variety of geometric structures; 57 exact solutions and the corresponding criteria have been obtained. A kind of new nonlinear hyperbolic wave which we call delta shock appears in some solutions. The delta shock is a discontinuity surface which is the support of a Dirac δ-function.