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

2002/05/16 by Ramon Plaza, Ramón G. Plaza, Plaza, Ramon +2
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #math.AP

paper · pdf · doi:10.48550/arxiv.math/0205180

47 pp Minor typos corrected from original version of May 15

openalex publication_date 2002/05/16 · arxiv created 2002/06/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Nonlinear asymptotic stability of viscous shock profiles for conservation laws

Related

• Stability of undercompressive viscous shock profiles of hyperbolic--parabolic systems
• Spectral stability of shock profiles for hyperbolically regularized systems of conservation laws
• Spectral stability of weak relaxation shock profiles
• Numerical proof of stability of viscous shock profiles
• Non-linear stability of shock profiles in dissipative hyperbolic-hyperbolic systems