We present a new a priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case. © 2009 Elsevier Masson SAS. All rights reserved.
|Original language||English (US)|
|Number of pages||16|
|Journal||Annales de l'Institut Henri Poincare (C) Non Linear Analysis|
|State||Published - Mar 2010|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-11-007-43
Acknowledgements: KF's work has been supported by the KAUST Award No. KUK-11-007-43, made by King Abdullah University of Science and Technology (KAUST). JAC was supported by the project MTM2008-06349-C03-03 of the Spanish Ministerio de Ciencia e Innovacion. LD was supported by the french project ANR CBDif. The authors acknowledge partial support of the trilateral project Austria-France-Spain (Austria: FR 05/2007 and ES 04/2007, Spain: HU2006-0025 and HF2006-0198, France: Picasso 13702TG and Amadeus 13785 UA). LD and KF also wish to acknowledge the kind hospitality of the CRM of Barcelona.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.