Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 01 January 1998 - Volume 128, Issue 04  

Research Article

Fragmentation–diffusion model. Existence of solutions and their asymptotic behaviour*

Philippe Laurençota1 and Dariusz Wrzoseka2

a1 Institut Elie Cartan-Nancy, Université de Nancy I, BP 239, F-54506 Vandœuvre les Nancy cedex, France e-mail: laurenco@iecn.u-nancy.fr

a2 Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2,02-097 Warszawa, Poland e-mail: darekw@appli.mimuw.edu.pl

Abstract

An infinite system of reaction–diffusion equations that represents a particular case of the discrete coagulation–fragmentation model with diffusion is studied. The reaction part of the model describes the rate of clusters break-up into smaller particles. Diffusion constants are assumed to be different in each equation and concentration-dependent fragmentation coefficients are considered. Existence of solutions is studied under fairly general assumptions on fragmentation coefficients and initial data. Uniqueness in the class of mass-preserving solutions is proved. Convergence of solutions to spatially homogeneous equilibrium state is obtained.

(Received February 12 1997)

Footnotes

* Both authors were supported by the French-Polish projects 558/1995 and 6058/1996. The second author was also partially supported by Polish KBN grant 2 PO3A 065 08