Singular solutions to the Riemann problem for a macroscopic production model.

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. [ABSTRACT FROM AUTHOR]