Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion
KAUST Grant NumberKUK-I1-007-43
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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 , 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.
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.
SponsorsJAC 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.
PublisherInforma UK Limited