Fast-reaction limit for the inhomogeneous Aizenman-Bak model
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
scientific article; zbMATH DE number 5300206