M. Williams
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.

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