Abstract
The LSW–theory of domain coarsening describes the evolution of the size distribution of a system of particles evolving by diffusional mass exchange to reduce their total surface area. We prove existence and uniqueness of solutions to an inhomogeneous extension of the LSW–model in unbounded domains. This model arises naturally as a homogenization limit of the underlying free boundary problem in the case of a system of particles for which the screening length (the effective range of particle interactions) is smaller than the system size. The crucial ingredients in the analysis are, first, to establish the screening property by showing that the corresponding Green’s function decreases exponentially over the relevant distances. Second, we have to control the mass fluxes between different regions to prevent aggregation of mass in few particles which would result in blow–up of the solution.
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