Nonlocalized modulation of periodic reaction diffusion waves: the Whitham equation

Mathew A. Johnson (1) , Pascal Noble (2) , Luis Miguel Miguel Rodrigues (2) , Kevin Zumbrun (3)

1 Department of Mathematics [Lawrence, Kansas]
2 ICJ - Institut Camille Jordan
3 Department of Mathematics IU

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 to leading order of a modulation whose parameter evolution is governed by an associated Whitham averaged equation.

Domaines: Equations aux dérivées partielles [math.AP]

Mathew A. Johnson, Pascal Noble, Luis Miguel Miguel Rodrigues, Kevin Zumbrun. Nonlocalized modulation of periodic reaction diffusion waves: the Whitham equation. Archive for Rational Mechanics and Analysis, 2013, 2, pp.669-692. ⟨hal-00943578⟩