A global existence theorem on weak solutions is shown for the continuous coagulation equation with collisional breakage under certain classes of unbounded collision kernel and distribution functions. The 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.

中文翻译：

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具有碰撞破坏的连续混凝模型的弱解

在某些类型的无界碰撞核和分布函数下，针对具有碰撞破坏的连续凝结方程，给出了弱解的整体存在性定理。该模型描述了当二元碰撞发生时通过聚结形成单个粒子或通过破裂（可能发生质量转移）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。