Nonlocalized Modulation of Periodic Reaction Diffusion Waves: Nonlinear Stability

Nonlocalized Modulation of Periodic Reaction Diffusion Waves: Nonlinear Stability

Extending results of Johnson and Zumbrun showing stability under localized ( L 1 ) 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 modulat...

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Veröffentlicht in:Archive for rational mechanics and analysis 2013-02, Vol.207 (2), p.693-715
Hauptverfasser: Johnson, Mathew A., Noble, Pascal, Rodrigues, L. Miguel, Zumbrun, Kevin
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Archives
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Mathematics
Physics
Physics and Astronomy
Theoretical
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Zusammenfassung:Extending results of Johnson and Zumbrun showing stability under localized ( L 1 ) 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 , where is the background profile and h 0 is the initial modulation.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-012-0573-9