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From the discrete to the continuous coagulation–fragmentation equations

Published online by Cambridge University Press:  12 July 2007

Philippe Laurençot  and
Stéphane Mischler
Philippe Laurençot
Affiliation:
Mathématiques pour l'Industrie et la Physique, CNRS UMR 5640, Université Paul Sabatier–Toulouse 3, 118 route de Narbonne, F-31062 Toulouse Cedex 4, France (laurencot@mip.ups-tlse.fr)
Stéphane Mischler
Affiliation:
Laboratoire de Mathématiques Appliquées, Université de Versailles–Saint Quentin, 45 avenue des Etats-Unis, F-78035 Versailles, France; DMA, CNRS UMR 8553, Ecole Normale Supérieure, 45 rue d'Ulm, F-75230 Paris Cedex 05, France (stephane.mischler@ens.fr)
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Abstract

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The connection between the discrete and the continuous coagulation–fragmentation models is investigated. A weak stability principle relying on a priori estimates and weak compactness in L1 is developed for the continuous model. We approximate the continuous model by a sequence of discrete models and, writing the discrete models as modified continuous ones, we prove the convergence of the latter towards the former with the help of the above-mentioned stability principle. Another application of this stability principle is the convergence of an explicit time and size discretization of the continuous coagulation-fragmentation model.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 5 , October 2002 , pp. 1219 - 1248
Copyright
Copyright © Royal Society of Edinburgh 2002