Fast-reaction limit for the inhomogeneous Aizenman-Bak model
type: Item
instance of: scholarly article
title: Fast-reaction limit for the inhomogeneous Aizenman-Bak model
zbMATH Open document ID: 1148.35302
published in: Kinetic and Related Models
publication date: 2008-07-11T00:00:00Z
review text: Solutions of the spatially inhomogeneous diffusive Aizenmann-Bak model [\textit{M. Aizenman} and \textit{T. A. Bak}, Commun. Math. Phys. 65, 203--230 (1979; Zbl 0458.76062)] for clustering within a bounded domain with homogeneous Neumann boundary conditions are shown to stabilize, in the fast reaction limit, towards local equilibria determined by their monomer density. Moreover, the sequence of monomer densities converges to the solution of a nonlinear diffusion equation whose nonlinearity depends on the size-dependent diffusion coefficient. Initial data are assumed to be integrable, bounded and with a certain number of moments in size. The number density of clusters for the solutions is assumed to verify uniform bounds away from zero and infinity independently of the scale parameter
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 82D60
zbMATH DE Number: 5300206
zbMATH Keywords: homogeneous Neumann boundary conditions
zbMATH Keywords: nonlinear diffusion equation
zbMATH Keywords: entropy-based estimates
zbMATH Keywords: duality arguments
zbMATH Keywords: coagulation-fragmentation equation
author: J. A. Carrillo
author: Laurent Desvillettes
author: Klemens Fellner
MaRDI profile type: Publication
full work available at URL: krm.2008.1.127
OpenAlex ID: W2320229498
DOI: 10.3934/KRM.2008.1.127
description: scientific article; zbMATH DE number 5300206