  We study an Eulerian droplet model which can be seen as the pressureless gas
system with a source term, a subsystem of this model and the inviscid Burgers
equation with source term. The condition for loss of regularity of a solution
to Burgers equation with source term is established. The same condition applies
to the Eulerian droplet model and its subsystem. The Riemann problem for the
Eulerian droplet model is constructively solved by going through the solution
of the Riemann problems for the inviscid Burgers equation with a source term
and the subsystem, respectively. Under suitable generalized Rankine-Hugoniot
relations and entropy condition, the existence of delta-shock solution is
established. The existence of a solution to the generalized Rankine-Hugoniot
conditions is proven. Some numerical illustrations are presented.
