Probability Seminar
Thursday, March 31, 2016, 4:30pm, 119 Physics
David Kaspar (Brown University)
Scalar conservation laws with Markov initial data
Abstract:- The inviscid Burgers' equation has the remarkable property
that its dynamics preserve the class of spectrally negative L\'{e}vy
initial data, as observed by Carraro and Duchon (statistical
solutions) and Bertoin (entropy solutions). Further, the evolution of
the L\'{e}vy measure admits a mean-field description, given by the
Smoluchowski coagulation equation with additive kernel. In this talk
we discuss ongoing efforts to generalize this result to scalar
conservation laws, a special case where this is done, and a connection
with integrable systems. Includes work with F. Rezakhanlou. [video]
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