Regularity and mass conservation for discrete coagulation–fragmentation equations with diffusion

Handle URI:
http://hdl.handle.net/10754/599486
Title:
Regularity and mass conservation for discrete coagulation–fragmentation equations with diffusion
Authors:
Cañizo, J.A.; Desvillettes, L.; Fellner, K.
Abstract:
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.
Citation:
Cañizo JA, Desvillettes L, Fellner K (2010) Regularity and mass conservation for discrete coagulation–fragmentation equations with diffusion. Annales de l’Institut Henri Poincare (C) Non Linear Analysis 27: 639–654. Available: http://dx.doi.org/10.1016/j.anihpc.2009.10.001.
Publisher:
Elsevier BV
Journal:
Annales de l'Institut Henri Poincare (C) Non Linear Analysis
KAUST Grant Number:
KUK-11-007-43
Issue Date:
Mar-2010
DOI:
10.1016/j.anihpc.2009.10.001
Type:
Article
ISSN:
0294-1449
Sponsors:
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorCañizo, J.A.en
dc.contributor.authorDesvillettes, L.en
dc.contributor.authorFellner, K.en
dc.date.accessioned2016-02-28T05:52:01Zen
dc.date.available2016-02-28T05:52:01Zen
dc.date.issued2010-03en
dc.identifier.citationCañizo JA, Desvillettes L, Fellner K (2010) Regularity and mass conservation for discrete coagulation–fragmentation equations with diffusion. Annales de l’Institut Henri Poincare (C) Non Linear Analysis 27: 639–654. Available: http://dx.doi.org/10.1016/j.anihpc.2009.10.001.en
dc.identifier.issn0294-1449en
dc.identifier.doi10.1016/j.anihpc.2009.10.001en
dc.identifier.urihttp://hdl.handle.net/10754/599486en
dc.description.abstractWe 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.en
dc.description.sponsorshipKF'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.en
dc.publisherElsevier BVen
dc.subjectDiscrete coagulation-fragmentation systemsen
dc.subjectDuality argumentsen
dc.subjectMass conservationen
dc.titleRegularity and mass conservation for discrete coagulation–fragmentation equations with diffusionen
dc.typeArticleen
dc.identifier.journalAnnales de l'Institut Henri Poincare (C) Non Linear Analysisen
dc.contributor.institutionUniversidad Autonoma de Barcelona, Barcelona, Spainen
dc.contributor.institutionEcole Normale Superieure de Cachan, Cachan, Franceen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
kaust.grant.numberKUK-11-007-43en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.