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Dynamics of kinematic aggregation equations

Connections for Women on Optimal Transport: Geometry and Dynamics August 22, 2013 - August 23, 2013

August 22, 2013 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Andrea Bertozzi (University of California, Los Angeles)
Location: SLMath: Eisenbud Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Abstract Aggregation equations are used to model nonlocal interactions in biology and related problems in which a population density moves with a velocity that depends nonlocally on the density through an aggregation interaction kernel. The mathematical behavior of these equations has direct connection to problems in optimal transport and incompressible fluid dynamics. I will review recent results for these problems and the role of geometry in the dynamics of both smooth and singular solutions
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