  We analyze the evolution of the distribution, both in the phase space and in
the physical space, of inertial particles released by a spatially-localized
(punctual) source and advected by an incompressible flow. The difference in
mass density between fluid and particles is assumed as small, and represents
the basic parameter for a regular perturbative expansion. By means of
analytical techniques such as Hermitianization, we derive a chain of equations
of the advection--diffusion--reaction type, easily solvable at least
numerically. Our procedure provides results also for finite particle inertia,
away from the over-damped limit of quasi-tracer dynamics.
