Shock waves

Monday, July 20, 2009 - 11:00am - 11:50am
Mikhail Feldman (University of Wisconsin, Madison)
In this talk we will start with discussion of shock reflection
phenomena. Then we describe recent results on existence and stability of global solutions to regular shock reflection for potential flow
for all wedge angles up to the sonic angle, and discuss the techniques.
The approach is to reduce the shock reflection problem to a free
boundary problem for a nonlinear elliptic equation, with ellipticity
degenerate near a part of the boundary (the sonic arc). We will discuss
Saturday, July 18, 2009 - 10:45am - 12:00pm
Kevin Zumbrun (Indiana University)
We discuss finally stability and bifurcation of flow in a channel with periodic boundary conditions: cellular bifurcation, pattern formation,
and an Evans function construction for genuinely multi-dimensional
(i.e., nonplanar) solutions.
Thursday, July 16, 2009 - 4:00pm - 5:00pm
Kevin Zumbrun (Indiana University)
Using a combination
of numerical Evans function computations and asymptotic ODE analysis,
we carry out global stability analyses for interesting examples including ideal gas and parallel MHD shocks, across the entire range
of physical parameters: in particular, in the large amplitude or
magnetic field limit.
Tuesday, July 14, 2009 - 2:00pm - 3:00pm
Kevin Zumbrun (Indiana University)
Course abstract: We examine from a classical dynamical systems point
of view stability, dynamics, and bifurcation of viscous shock waves and related solutions of nonlinear pde.

Lecture 1 abstract: Stability of viscous shock waves. We discuss the
basic types of viscous shock waves, the Evans function condition
and its meaning, and outline a basic one-dimensional stability proof assuming that the Evans condition holds.
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