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Propagation of special initial data through Burgers' equation

Semester: 
Spring 2016
Seminar Date: 
Monday, April 25 1:30pm - 6:15pm at Brown
Speaker: 
Carey Caginalp (Brown)

A problem of great interest regarding conservation laws is the propagation of certain special initial data, and in particular, the behavior and evolution of the solution. For example, if we start with initial data in the form of a Markov process (in $x$), will this property continue to be preserved in time? What about other more general classes of initial data? I aim to address this and other questions, as well as provide some insight into the so-called $n$-point equations, the relationships between positions and velocities at certain points.