New developments of delta shock waves and its applications in systems of conservation laws (Q424426)

The authors develop the theory of delta shock type solutions to the \(2\times 2\) system of conservation laws \(u_t+(\phi(r)u)_x=v_t+(\phi(r)v)_x=0\), where \(r=au+bv\) with some constants \(a,b\). Both state variables \(u,v\) may contain delta shocks. The generalized Rankine-Hugoniot relation and the entropy condition are proposed, the existence and uniqueness of delta shock type solutions of the Riemann problem are established. The authors also prove the existence and convergence of viscous approximations. Some applications to known systems are given, numerical simulations are presented.