Singular solutions to the Riemann problem for a macroscopic production model

Source abstract

This paper is devoted to the Riemann problem for the data‐fitted second‐order macroscopic production model when one of the Riemann initial data is at a vacuum state or at rest. The Riemann solutions are constructed completely by using the continuous method with respect to the initial data, which include some non‐classical waves such as the delta standing wave and the superposition of a shock wave and a contact discontinuity etc. In addition, an example is given to explain the wave interaction problem when the vacuum state is involved.