Well-posedness for a coagulation multiple-fragmentation equation

Eduardo Cepeda (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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 total fragmentation rate, in particular an infinite number of fragments, is considered. 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.

Mots clés: Coalescence; Interacting stochastic particle systems.; Coagulation Multi-Fragmentation equation

Domaines: Equations aux dérivées partielles [math.AP]

Eduardo Cepeda. Well-posedness for a coagulation multiple-fragmentation equation. Differential and integral equations, 2014, 27 (1/2), pp.105-136. ⟨hal-00772026v2⟩