 
Summary: CoagulationFragmentation Processes
Herbert Amann
Abstract. We study the wellposedness of coagulationfragmentation mod
els with diusion for large systems of particles. The continuous and the
discrete case are considered simultaneously. In the discrete situation we are
concerned with a countable system of coupled reactiondiusion equations,
whereas the continuous case amounts to an uncountable system of such
equations. These problems can be handled by interpreting them as abstract
vectorvalued parabolic evolution equations, where the dependent variables
take values in innitedimensional Banach spaces. Given suitable assump
tions, we prove existence and uniqueness in the class of volume preserving
solutions. We also derive suÆcient conditions for global existence.
1. Introduction
In recent years, much eort has been put into the mathematical foun
dation of cluster growth. In this theory it is assumed that the system under
consideration consists of a very large number of particles that can coagu
late to form clusters, which in turn, can merge to form larger clusters or can
break apart into smaller ones. Models of cluster growth arise in a variety of
situations, for example in aerosol science, atmospheric physics, astrophysics,
colloidal chemistry, polymer science, hematology, and biology. The aim of
