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{\bf Coarsening in nonlocal interfacial systems}

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Dejan Slepcev\\
Carnegie Mellon University\\
Department of Mathematical Sciences\\
Pittsburgh, PA  15213\\
slepcev@andrew.cmu.edu
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\noindent {\bf 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.

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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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