English

Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation

Analysis of PDEs 2015-05-28 v3

Abstract

In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized perturbation. Here, we determine time-asymptotic behavior under such perturbations, showing that solutions consist to leading order of a modulation whose parameter evolution is governed by an associated Whitham averaged equation.

Keywords

Cite

@article{arxiv.1105.5044,
  title  = {Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation},
  author = {Mathew Johnson and Pascal Noble and L. Miguel Rodrigues and Kevin Zumbrun},
  journal= {arXiv preprint arXiv:1105.5044},
  year   = {2015}
}