Riemann Problem and Wave Interactions for a Temple-class Hyperbolic System of Conservation Laws

The exact solutions of the Riemann problem for a Temple-class hyperbolic system of conservation laws consisting of three scalar equations are obtained in fully explicit forms, in which all the state variables may contain Dirac delta functions simultaneously under some suitable Riemann initial data. The generalized Rankine–Hugoniot conditions and the over-compressive entropy condition are derived for such very singular delta shock wave solution. We also prove rigorously this delta shock wave solution satisfying the system in the sense of distributions. Moreover, three typical cases for the delta shock interaction problem are provided in order to illustrate some interesting nonlinear wave phenomena. In addition, some numerical simulations are offered to confirm the theoretical results.