 
Summary: On a quasilinear coagulationfragmentation
model with diusion
Herbert Amann and Frank Weber
Abstract We consider a system of a very large number of particles of very dierent sizes, sus
pended in a carrier
uid. These particles move due to diusion and superimposed transport
processes, merge to form larger clusters, or fragment into smaller ones.
In the present paper a mathematical model for such processes is derived, consisting of an
innite quasilinear reactiondiusion system, coupled to the Navier Stokes equations for the
motion of the suspension. We prove the wellposedness of this problem, derive a positivity
result, and show that the total mass of the suspended particles is conserved.
1 Introduction
The aim of this paper is to discuss the wellposedness of a mathematical model describing
cluster growth. More precisely, we consider a very large number of particles of very dierent
sizes, suspended in a carrier
uid. These particles, which are also called clusters, can coagu
late to form larger particles, or fragment into smaller ones. Moreover, the clusters move due
to diusion and superimposed transport processes.
We describe this system by means of the particle size distribution function, which is
a density measuring the number of clusters of a given size y at place x and time t. Two
situations are considered simultaneously: the discrete case, where each cluster consists of an
integer number of elementary particles, and the continuous case. Accordingly, in the discrete
