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Seminar Abstracts

Laurent Thomas, UCLA

Blowup in multidimentional aggregation equation

Abstract: We consider the conservation law u_t+div(uv)=0 where the velocity field is defined via a convolution: v=-grad K*u. We will determine the exact amount of singularity needed on the interaction potential K in order to generate finite time blow-up. To be more precise, we will show that if K satisfies some Osgood condition, then L^p solutions of the PDE exist for all time, whereas if the Osgood condition is not satisfied, compactly supported solutions collapse to a delta function in finite time.

TUESDAY,April 28, 2009
Time: 1:30 P.M.
Location: PPB 300