'Society for Industrial & Applied Mathematics (SIAM)'
Doi
Abstract
This is the published version, also available here: http://dx.doi.org/10.1137/100781808.Extending results of Oh and Zumbrun in dimensions d≥3, we establish nonlinear stability and asymptotic behavior of spatially periodic traveling-wave solutions of viscous systems of conservation laws in critical dimensions d=1,2, under a natural set of spectral stability assumptions introduced by Schneider in the setting of reaction diffusion equations. The key new steps in the analysis beyond that in dimensions d≥3 are a refined Green function estimate separating off translation as the slowest decaying linear mode and a novel scheme for detecting cancellation at the level of the nonlinear iteration in the Duhamel representation of a modulated periodic wave