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

J. A. Carrillo, L. Desvillettes, K. Fellner

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2 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)1338-1351
Number of pages14
JournalCommunications in Partial Differential Equations
Volume34
Issue number11
DOIs
StatePublished - Oct 30 2009
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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