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An Evans function approach to spectral stability of small-amplitude shock profiles

Ramon Plaza·Kevin Zumbrun
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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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Ramon Plaza, Kevin Zumbrun. 2002-06-02. An Evans function approach to spectral stability of small-amplitude shock profiles. https://arxiv.org/abs/math/0205180

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