K. Zumbrun
Planar Stability Criteria for Multidimensional Viscous Shock Waves

Hyperbolic Systems of Balance Laws - Cetraro July 14-21, 2003

We present recent developments in the stability theory for planar viscous shock waves. Planned topics include: Evans function framework, uniformly stable shocks and their large-time behavior, weakly stable shocks and transition to instability, stability of small-amplitude Lax and overcompressive shocks. The emphasis will be on applications to physical models, with ``real,'' or partial viscosity. The planar assumption makes possible a concrete analysis based on Evans function techniques and explicit estimatation of the Laplace and Fourier inversion formulae. This course is intended to be complementary to that of M. Williams, which treats more general (nonplanar) shock fronts from a somewhat more abstract point of view.

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