On Global Asymptotic Stability for the diffusive Carr-Penrose Model

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 $β$ with $0<β\le 1$. It is shown that if the initial data has compact support then the solution to the diffusive model at large time approximates the $β=1$ self-similar solution. This result supports the intuition that diffusion provides the mechanism whereby the $β=1$ self-similar solution of the LSW model is the only physically relevant one.

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