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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Carey Caginalp
Carnegie Mellon University
Title: Conservation Laws, Shocks, and Random Initial Conditions

Abstract: Conservation laws have a wide range of applications to problems in fluid mechanics, turbulence, kinetic theory and many others. As perhaps the simplest quasilinear PDE, Burgers' equation has an important role as a prototype or test case for analysis for qualitative properties. I will discuss two related probabilistic approaches for which one can model the evolution of shocks through objects known as n-point functions, generalized analogs of a probability density for the solution at various points. In the second approach, I will illustrate how this method leads to solutions that persist through shock interactions, without need for any sort of resetting procedure, which is required for many methods.

Date: Tuesday, September 19, 2017
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  David Kinderlehrer