Pointwise nonlinear stability of nonlocalized modulated periodic reaction–diffusion waves

In this paper, extending previous results of [2], we obtain pointwise nonlinear stability of periodic traveling reaction–diffusion waves, assuming spectral linearized stability, under nonlocalized perturbations. More precisely, we establish pointwise estimate of nonlocalized modulational perturbation under a small initial perturbation consisting of a nonlocalized modulation plus a localized perturbation decaying algebraically.