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

Published online by Cambridge University Press:  14 November 2011

Philippe Laurençot  and
Dariusz Wrzosek
Philippe Laurençot
Affiliation:
Institut Elie Cartan-Nancy, Université de Nancy I, BP 239, F-54506 Vandœuvre les Nancy cedex, France e-mail: laurenco@iecn.u-nancy.fr
Dariusz Wrzosek
Affiliation:
Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2,02-097 Warszawa, Poland e-mail: darekw@appli.mimuw.edu.pl
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 4 , 1998 , pp. 759 - 774
Copyright
Copyright © Royal Society of Edinburgh 1998

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