**Dynamics in classical mean-field models for Ostwald ripening**

Ostwald Ripening, a fundamental process in the aging of materials,
denotes the last stage in a phase transition
in binary mixtures. Particles of a new phase interact to reduce
their total surface energy. As a result larger particles grow
at the expense of smaller one, which results in a coarsening
of the microstructure.
An important feature of this process is its statistical
self-similarity, which means that
the patterns at different times look identical after rescaled
by one typical length scale.

In the nowadays classical theory by Lifshitz-Slyozov and Wagner
("LSW") this process is described by a nonlocal
evolution equation for the
particle size distribution. For this model universal self-similar
large-time behavior is predicted.
However, a mathematically rigorous analysis reveals that in strong
contrast to these predictions the large time dynamics are not
universal but depend sensitively on the initial data.
We will give an overview of the results on the long-time dynamics
of the LSW model and will also discuss possible mechanisms
which could provide a regularization of the model which overcomes
the above described weak selection problem.

* Barbara Niethammer*

Back to Colloquium Page