Abstract: Abstract: We consider coarsening in interfacial systems driven by nonlocal energies. Of particular interest are the nonlocal Cahn-Hilliard equation and models of biological aggregation. The energies considered cause the system to separate into phases. The pattern of interfaces evolves under nonlocal surface-tension-type effects. The typical length scales grow and the pattern coarsens. We prove a rigorous upper bound on the coarsening rate.
The proof uses the energy-based approach to estimates on rate of coarsening introduced by Kohn and Otto. To show the required estimates on the flatness of the energy landscape we develop a geometric approach which is applicable to a wider class of problems, which includes ones based on local, gradient type energies.
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