 
Summary: COAGULATIONFRAGMENTATION
MODELS WITH DIFFUSION
Herbert Amann
Institute for Mathematics, University of Zurich
Winterthurerstr. 190, CH8057 Zurich, Switzerland
Consider systems of a very large number of particles, being suspended in a
uid, for example, which can diuse and coagulate to form clusters that, 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, atmo
spheric physics, colloidal chemistry, or polymer science, etc. The theory originates
in the work of M.V. Smoluchowski [9], [10] and has found various generalizations,
extensions, and applications in the physical literature (e.g., [5], [6]).
The Model. The aim of the theory is the description of the particle size distri
bution function u as a function of time and space as the system undergoes changes
due to various physical in
uences.
The equations under consideration are of the form
@ t u r (a a aru + ~au) + a 0 u = [@ t u] coag + [@ t u] frag ; (1)
where the coagulation term [@ t u] coag is given by
[@ t u] coag (y) = 1
2
