Delta Shock Wave in a Perfect Fluid Model with Zero Pressure

What is it about?

The Riemann problem for a perfect fluid model with zero pressure is considered, where the external force is a given continuous function of time. All of exact solutions are given. In particular, a vacuum occurs in the solutions, although initial data stay far away from the vacuum. It is shown that a delta shock wave in which density and internal energy contain a Dirac delta function develops in the solutions. The position, velocity, and weights of the delta shock wave are presented explicitly. Moreover, all of the solutions are not self-similar because of the presence of the external force.

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