The sonic line as a free boundary: Stability under<br/><br/>perturbations

Friday, July 31, 2009 - 11:00am - 11:50am
EE/CS 3-180
Barbara Keyfitz (The Ohio State University)
The study of self-similar solutions of multidimensional conservation laws
leads to systems of equations that change type.
Change of type occurs either across a transonic shock or
at a sonic line. Often the sonic line appears as a free boundary in
the formulation of the problem. Some recent numerical (and experimental)
discoveries of a new kind of shock reflection ('Guderley Mach reflection')
lead to interesting and still unresolved questions concerning the nature
of the self-similar solutions in this generic case.

In this talk, I will present some analysis of a simple model for this
phenomenon, using the transonic small disturbance equation. The
simplified problem seems amenable to analysis, but we are just beginning
to make progress. This is a report on current joint work with Allen
Tesdall and Kevin Payne.
MSC Code: