On the “Vacuum” Dam-Break Problem: Exact Solutions and Their Long Time Asymptotics

The classical dam-break problem for the shallow water system with a dry/vacuum downstream state is revisited in the context of exact solutions which generalize the Riemann setup of a Heaviside jump between constant states to continuous initial data. Two main setups are considered, chosen to illustrate how local properties of the dependent variables at the vacuum point influence the evolution over different time scales. For the first case, the...