Self-Similar Behaviour for Noncompactly Supported Solutions of the LSW Model

In this paper a method of approximating the classical LSW model near self-similar solutions for initial data with infinite support is developed. The resulting problem is an integrodifferential equation having two time scales that can be studied using multiple scale methods. The analysis provides a detailed description of the precise manner in which the characteristics “leak” through the critical radius associated to the self-similar solutions. The analysis in this paper makes precise the meaning of the iterated logarithmic asymptotics in the dynamics of the LSW model that were already obtained in the original Lifshitz-Slyozov paper. Examples of noncompactly supported solutions of the LSW model that do not behave in a self-similar manner are also given.