On Global Asymptotic Stability for the Diffusive Carr–Penrose Model

Abstract

This paper is concerned with large time behavior of the solution to a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. Like the LSW model, the Carr–Penrose model has a family of rapidly decreasing self-similar solutions, depending on a parameter \(\beta \) with \(0<\beta \le 1\). It is shown that if the initial data have compact support, then the solution to the diffusive model at large time approximates the \(\beta =1\) self-similar solution. This result supports the intuition that diffusion provides the mechanism whereby the \(\beta =1\) self-similar solution of the LSW model is the only physically relevant one.