Well-posedness for a coagulation multiple-fragmentation equation
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 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.
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