Nonlocalized modulation of periodic reaction diffusion waves: Nonlinear stability

2011/05/31 by Mathew Johnson, Pascal Noble, L. Miguel Rodrigues +1 · 1 citation
Mathematics · #math.AP

paper · pdf · doi:10.1007/s00205-012-0573-9

arxiv created 2011/06/23 · arxiv updated 2015/05/28

Abstract

By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized perturbation. The main new ingredient is a detailed analysis of linear behavior under modulational data u'(x)h₀(x), where u is the background profile and h₀ is the initial modulation

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