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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 |