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Coagulation-Fragmentation Processes Herbert Amann
 

Summary: Coagulation-Fragmentation Processes
Herbert Amann
Abstract. We study the well-posedness of coagulation-fragmentation mod-
els with di usion 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 reaction-di usion equations,
whereas the continuous case amounts to an uncountable system of such
equations. These problems can be handled by interpreting them as abstract
vector-valued parabolic evolution equations, where the dependent variables
take values in in nite-dimensional 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 e ort 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

  

Source: Amann, Herbert - Institut für Mathematik, Universität Zürich

 

Collections: Mathematics