Stability of Multidimensional Viscous Shocks
Hyperbolic Systems of Balance Laws - Cetraro July 14-21, 2003
The goal of the course will be to present recent results on the stability of
multiD viscous shocks for systems of conservation laws (joint work with
O. Gues, G. Metivier, and K.Zumbrun.
In particular, we discuss the rigorous validity of the small viscosity limit
for multiD curved shocks (a short time result), and the long time stability
of multiD planar viscous shocks.
The approach to both problems is a unified one based on energy estimates
derived through the use of degenerate Kreiss type symmetrizers.
Along the way we'll present the needed background on Kreiss symmetrizers,
pseudodifferential operators, inviscid shock theory and Evans functions.