The Coagulation - Fragmentation Equation and its Stochastic Counterpart
Résumé
We consider a coagulation multiple-fragmentation equation, which describes the concentration $c_t(x)$ of particles of mass $x \in (0,\infty)$ at the instant $t \geq 0$ in a model where fragmentation and coalescence phenomena occur. We study the existence and uniqueness of measured-valued solutions to this equation for homogeneous-like kernels of homogeneity parameter $\lambda \in (0,1]$ and bounded fragmentation kernels, although a possibly infinite number of fragments is considered. We also study a stochastic counterpart of this equation where a similar result is shown. We ask to the initial state to have a finite $\lambda$-moment. This work relies on the use of a Wasserstein-type distance, which has shown to be particularly well-adapted to coalescence phenomena. It was introduced in previous works on coagulation and coalescence.
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