Blow-up in multidimensional aggregation equations

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• Thomas Laurent (UCLA)
• Tuesday 09 February 2010, 16:00-17:00
• MR14, CMS.

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The aggregation equation is a continuum model for interacting particle systems with attractive/repulsive pairwise interaction potential K. It arises in a number of models for biological aggregation, materials science and granular media. The main phenomenon of interest is that, even with smooth initial data, the solutions can concentrate mass in finite time (i.e. a delta Dirac appears in the solution in finite time). Using techniques from fluid dynamics and from optimal transport, we prove rigorous results which explain how and under what circumstances these Dirac delta functions appear.

This talk is part of the Applied and Computational Analysis series.

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