Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation

By Mathew A. Johnson, P. Noble, L. M. Rodrigues, Kevin Zumbrun. 2011

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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 (L1) perturbation. Here, we determine time-asymptotic behavior under such perturbations, showing that solutions consist of a leading order of a modulation whose parameter evolution is governed by an associated Whitham averaged equation.

Subfields: Computer Networks and Communications, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c16f062fb8fa1606c51fa7ace973f9c140b929dd