  We consider the dynamics of a collection of particles that interact pairwise
and are restricted to move along the real line. Moreover, we focus on the
situation in which particles undergo perfectly inelastic collisions when they
collide. The equations of motion are a pair of partial differential equations
for the particles' mass distribution and local velocity. We show that solutions
of this system exist for given initial conditions by rephrasing these equations
in Lagrangian coordinates and then by solving for the associated trajectory
map.
