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Research Seminar: Scalar conservation laws with random data November 18, 2015 (10:00 AM PST - 11:30 AM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Govind Menon (Brown University)
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Ensembles of solutions to partial differential equations underly mathematical theories of turbulence and phase transitions. However, our understanding of such ensembles for even well-understood PDE is quite modest. This should be expected, since in rigorous terms, an "ensemble" is a probability measure supported on the space of solutions.


I will describe several results on the deterministic evolution of spatially random data by scalar conservation laws with a convex flux. The (surprising) punchline is that the evolution of the law of the solution is determined by a completely integrable system of kinetic equations that describes the clustering of shocks. 

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