Existence and uniqueness of weak solutions to the singular kernels coagulation equation with collisional breakage

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.