An Evans function approach to spectral stability of small-amplitude shock profiles
Ramon Plaza, Kevin Zumbrun
Abstract
We establish one-dimensional spectral stability of small amplitude viscous and relaxation shock profiles using Evans function techniques to perform a series of reductions and normal forms to reduce to the case of the scalar Burgers equation. In multidimensions, the canonical behavior is described, rather by a 2x2 viscous conservation law; this case will be treated in a companion paper by similar techniques.
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