Solutions of the 3-D transportation equations

In this paper, the transportation equations art? considered. The Riemann problem in three space dimensions for the transportation equations has been served analytically. Under the generalized Rankine-Hugoniot and entropy conditions, the existence and uniqueness of solutions involving constant states, slip surfaces (contact discontinuous) (J), Dirac delta waves (delta-waves), and vacuums (Vac) have been established. We prove that the weighted Dirac delta waves are distribution solutions of the 3-D transportation equations.