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We study the coarsening rates for attachment-limited kinetics which is modeled by nonlocal mean-curvature flow. Attachment-limited kinetics is observed during solidification processes, in which the system is divided into two domains of the two pure phases, more precisely islands of a solid phase surrounded by an undercooled liquid phase, and the relaxation process is due to material redistribution form high to low interfacial curvature regions. The interfacial area between the phases decreases in time while the volume of each phase is preserved. Consequently, the domain morphology coarsens. Experiments, heuristics and numerics suggest that the typical domain size
In this paper, we prove a weak one-sided version of this coarsening rate, namely we prove that