  We study a kinetic mean-field equation for a system of particles with
different sizes, in which particles are allowed to coagulate only if their
sizes sum up to a prescribed time-dependent value. We prove well-posedness of
this model, study the existence of self-similar solutions, and analyze the
large-time behavior mostly by numerical simulations. Depending on the parameter
$\Dconst$, which controls the probability of coagulation, we observe two
different scenarios: For $\Dconst>2$ there exist two self-similar solutions to
the mean field equation, of which one is unstable. In numerical simulations we
observe that for all initial data the rescaled solutions converge to the stable
self-similar solution. For $\Dconst<2$, however, no self-similar behavior
occurs as the solutions converge in the original variables to a limit that
depends strongly on the initial data. We prove rigorously a corresponding
statement for $\Dconst\in (0,1/3)$. Simulations for the cross-over case
$\Dconst=2$ are not completely conclusive, but indicate that, depending on the
initial data, part of the mass evolves in a self-similar fashion whereas
another part of the mass remains in the small particles.
