  A global existence theorem on weak solutions is shown for the continuous
coagulation equation with collisional breakage under certain classes of
unbounded collision kernels and distribution functions. This model describes
the dynamics of particle growth when binary collisions occur to form either a
single particle via coalescence or two/more particles via breakup with possible
transfer of mass. Each of these processes may take place with a suitably
assigned probability depending on the volume of particles participating in the
collision. The distribution function may have a possibility to attain an
algebraic singularity for small volumes.
