-Nonlinear Stability of Nonlocalized Modulated Periodic Reaction-Diffusion Waves

Soyeun Jung

Advances in Mathematical Physics, 2017, vol. 2017, 1-7

Abstract:

Assuming spectral stability conditions of periodic reaction-diffusion waves , we consider -nonlinear stability of modulated periodic reaction-diffusion waves, that is, modulational stability, under localized small initial perturbations with nonlocalized initial modulations. -nonlinear stability of such waves has been studied in Johnson et al. (2013) for by using Hausdorff-Young inequality. In this note, by using the pointwise estimates obtained in Jung, (2012) and Jung and Zumbrun (2016), we extend -nonlinear stability ( ) in Johnson et al. (2013) to -nonlinear stability. More precisely, we obtain -estimates of modulated perturbations of with a phase function under small initial perturbations consisting of localized initial perturbations and nonlocalized initial modulations .

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:3824501

DOI: 10.1155/2017/3824501

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