English

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

Analysis of PDEs 2007-05-23 v3

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.

Cite

@article{arxiv.math/0205180,
  title  = {An Evans function approach to spectral stability of small-amplitude shock profiles},
  author = {Ramon Plaza and Kevin Zumbrun},
  journal= {arXiv preprint arXiv:math/0205180},
  year   = {2007}
}

Comments

47 pp Minor typos corrected from original version of May 15

R2 v1 2026-07-22T16:45:25.958Z