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.

具有碰撞破坏的连续凝结方程解释了当粒子经历二元碰撞以通过聚结形成单个粒子或通过破裂并可能发生物质转移而形成两个/多个粒子时，粒子生长的动力学。这些过程中的每一个都可以根据参与碰撞的粒子的体积以适当分配的概率进行。在本文中，针对具有碰撞破坏的连续凝结方程的整体弱解被公式化为碰撞核和分布函数，它们允许在原点附近具有奇异性。特别地，证明依赖于经典弱\（L ^ 1 \）紧凑方法施加到适当选择的近似方程。在冲突内核的类更受限制的情况下，还考虑了唯一性问题。