On the interaction of δ-shocks and contact vacuum states

We study the pressureless gas equations, with piecewise constant initial data. In the immediate solution, δ-shocks and contact vacuum states arise and even meet (interact) eventually. A solution beyond the “interaction” is constructed. It shows that the δ-shock will continue with the velocity it attained instantaneously before the time of interaction, and similarly, the contact vacuum state will move past the δ-shock with a velocity value prior to the interaction. We call this the “no-effect-from-interaction” solution.