L1(R)-Nonlinear Stability of Nonlocalized Modulated Periodic Reaction-Diffusion Waves

Abstract

Assuming spectral stability conditions of periodic reaction-diffusion waves ( ), we consider 1 (R)-nonlinear stability of modulated periodic reaction-diffusion waves, that is, modulational stability, under localized small initial perturbations with nonlocalized initial modulations. (R)-nonlinear stability of such waves has been studied in for ≥ 2 by using Hausdorff-Young inequality. In this note, by using the pointwise estimates obtained in Jung, (2012)