  In this article, we investigate the existence and uniqueness of weak
solutions to the continuous coagulation equation with collisional breakage for
a class of unbounded collision kernels and distribution function. The collision
kernels and distribution functions may have a singularity on both the
coordinate axes. The proof of the existence result is based on a classical weak
L^1 compactness method applied to suitably chosen to approximate equations. The
question of uniqueness is also shown for some restricted class of collision
kernels.
