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

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

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
Pages (from-to)1338-1351
JournalCommunications in Partial Differential Equations
Volume34
DOIs
Publication statusPublished - 1 Nov 2009

Keywords

  • Coagulation-breakup equation
  • Duality arguments
  • Entropy-based estimates
  • Fast-reaction limit
  • Nonlinear diffusion equations

Fingerprint Dive into the research topics of 'Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion'. Together they form a unique fingerprint.

  • Cite this