Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case

TL;DR

This paper proves that spectral stability guarantees both linear and nonlinear stability of periodic traveling waves in viscous conservation law systems, removing previous restrictions on wave speed variations.

Contribution

It extends prior results by removing the assumption that wave speed must be constant to first order along the solution manifold.

Findings

Spectral stability implies linearized stability

Spectral stability implies nonlinear stability

Removes previous restrictions on wave speed variation

Abstract

Extending previous results of Oh--Zumbrun and Johnson--Zumbrun, we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling-wave solutions of viscous systems of conservation laws for systems of generic type, removing a restrictive assumption that wave speed be constant to first order along the manifold of nearby periodic solutions.