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The discrete coagulation equations with collisional breakage. (English) Zbl 1126.82320

Summary: The discrete coagulation equations with collisional breakage describe the dynamics of cluster growth when clusters undergo binary collisions resulting either in coalescence or breakup with possible transfer of matter. Each of these two events may happen with an a priori prescribed probability depending for instance on the sizes of the colliding clusters. We study the existence, density conservation and uniqueness of solutions. We also consider the large time behaviour and discuss the possibility of the occurrence of gelation in some particular cases.

MSC:

82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
34A34 Nonlinear ordinary differential equations and systems
34C60 Qualitative investigation and simulation of ordinary differential equation models
82C22 Interacting particle systems in time-dependent statistical mechanics
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