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On a quasilinear coagulation-fragmentation model with di usion
 

Summary: On a quasilinear coagulation-fragmentation
model with di usion
Herbert Amann and Frank Weber
Abstract We consider a system of a very large number of particles of very di erent sizes, sus-
pended in a carrier uid. These particles move due to di usion 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
in nite quasilinear reaction-di usion system, coupled to the Navier Stokes equations for the
motion of the suspension. We prove the well-posedness 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 well-posedness of a mathematical model describing
cluster growth. More precisely, we consider a very large number of particles of very di erent
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 di usion 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

  

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

 

Collections: Mathematics