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

The continuous coagulation equation with collisional breakage explains the dynamics of particle growth when particles experience binary collisions to form either a single particle via coalescence or two/more particles via breakup with possible transfer of matter. Each of these processes may take place with a suitably assigned probability depending on the volume of particles participating in the collision. In this article, global weak solutions to the continuous coagulation equation with collisional breakage are formulated to the collision kernels and distribution functions admitting a singularity near the origin. In particular, the proof relies on a classical weak L 1 compactness method applied to suitably chosen approximate equations. The question of uniqueness is also contemplated under more restricted class of collision kernels.