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2008, Volume 1, Issue 1: 127-137. Doi: 10.3934/krm.2008.1.127
This issue Previous Article Discrete transparent boundary conditions for the Schrodinger equation -- a compact higher order scheme Next Article Low field regime for the relativistic Vlasov-Maxwell-Fokker-Planck system; the one and one half dimensional case

Fast-reaction limit for the inhomogeneous Aizenman-Bak model

  • 1.

    ICREA-Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra

  • 2.

    ENS Cachan, CMLA, IUF & CNRS, PRES UniverSud, 61, Av. du Pdt Wilson, 94235 Cachan Cedex

  • 3.

    Faculty of Mathematics, University of Vienna, Nordbergstr. 15, 1090 Wien

Received:  October 2007
Revised:  October 2007
Published:  March 2008
Abstract Related Papers Cited by
    Abstract
  • Solutions of the spatially inhomogeneous diffusive\linebreak Aizenmann-Bak model 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: 35B40, 35Q72, 82D60.

    Citation:
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