Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion
Carrillo de la Plata, José Antonio (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Desvillettes, L. (École Normale Supérieure de Cachan (Cachan, França))
Fellner, K. (University of Cambridge. Department of Applied Mathematics and Theoretical Physics)
Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica

Imprint: Centre de Recerca Matemàtica 2009
Description: 15 p.
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 [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.
Rights: Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús Creative Commons
Language: Anglès
Series: Centre de Recerca Matemàtica. Prepublicacions
Series: Prepublicacions del Centre de Recerca Matemàtica ; 887
Document: article ; submittedVersion
Subject: Entropia ; Equacions no lineals ; Dualitat, Teoria de la (Matemàtica)

Adreça alternativa: https://hdl.handle.net/2072/46771


15 p, 204.6 KB

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Research literature > Preprints

 Record created 2010-04-14, last modified 2020-11-19



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