ON A DIFFUSIVE VERSION OF THE LIFSCHITZ-SLYOZOV-WAGNER EQUATION
Joseph G. Conlon · 2010
Abstract. This paper is concerned with the Becker-Döring (BD) system of equations and their relationship to the Lifschitz-Slyozov-Wagner (LSW) equations. A diffusive version of the LSW equations is derived from the BD equations. Existence and uniqueness theorems for this diffusive LSW system are proved. The major part of the paper is taken up with proving that solutions of the diffusive LSW system converge in the zero diffusion limit to solutions of the classical LSW system. In particular, it is shown that the rate of coarsening for the diffusive system converges to the rate of coarsening for the classical system. 1. Introduction. In this paper we shall be concerned with the Becker-Döring (BD) system of equations [2] and their relationship to the Lifschitz-Slyozov-Wagner (LSW) equations [11, 22]. The BD equations describe the time evolution for a mean field model of a population of particle clusters. Particle clusters are characterized by their volume