Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion

Handle URI:
http://hdl.handle.net/10754/599514
Title:
Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion
Authors:
Carrillo, J. A.; Desvillettes, L.; Fellner, K.
Abstract:
Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.
Citation:
Carrillo JA, Desvillettes L, Fellner K (2009) Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion. Communications in Partial Differential Equations 34: 1338–1351. Available: http://dx.doi.org/10.1080/03605300903225396.
Publisher:
Informa UK Limited
Journal:
Communications in Partial Differential Equations
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
30-Oct-2009
DOI:
10.1080/03605300903225396
Type:
Article
ISSN:
0360-5302; 1532-4133
Sponsors:
JAC acknowledges the support from DGI-MEC (Spain) project MTM2008-06349-C03-03 and 2009-SGR-345 from AGAUR-Generalitat de Catalunya. KF has partly been supported by the KAUST Investigator Award No. KUK-I1-007-43 of Peter A. Markowich. 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). KF and LD thank the CRM of Barcelona for its kind hospitality during part of the preparation of this work.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorCarrillo, J. A.en
dc.contributor.authorDesvillettes, L.en
dc.contributor.authorFellner, K.en
dc.date.accessioned2016-02-28T05:52:33Zen
dc.date.available2016-02-28T05:52:33Zen
dc.date.issued2009-10-30en
dc.identifier.citationCarrillo JA, Desvillettes L, Fellner K (2009) Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion. Communications in Partial Differential Equations 34: 1338–1351. Available: http://dx.doi.org/10.1080/03605300903225396.en
dc.identifier.issn0360-5302en
dc.identifier.issn1532-4133en
dc.identifier.doi10.1080/03605300903225396en
dc.identifier.urihttp://hdl.handle.net/10754/599514en
dc.description.abstractWeak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.en
dc.description.sponsorshipJAC acknowledges the support from DGI-MEC (Spain) project MTM2008-06349-C03-03 and 2009-SGR-345 from AGAUR-Generalitat de Catalunya. KF has partly been supported by the KAUST Investigator Award No. KUK-I1-007-43 of Peter A. Markowich. 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). KF and LD thank the CRM of Barcelona for its kind hospitality during part of the preparation of this work.en
dc.publisherInforma UK Limiteden
dc.subjectCoagulation-breakup equationen
dc.subjectDuality argumentsen
dc.subjectEntropy-based estimatesen
dc.subjectFast-reaction limiten
dc.subjectNonlinear diffusion equationsen
dc.titleRigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusionen
dc.typeArticleen
dc.identifier.journalCommunications in Partial Differential Equationsen
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-I1-007-43en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.