Nonlinear Stability and Asymptotic Behavior of Periodic Wave Trains in Reaction–Diffusion Systems Against $$C_{\textrm{ub}}$$-perturbations
Björn de Rijk
Abstract:We present a nonlinear stability theory for periodic wave trains in reaction–diffusion systems, which relies on pure $$L^\infty $$
L
∞
-estimates only. Our analysis shows that localization or periodicity requirements on perturbations, as present in the current literature, can be completely lifted. Inspired by previous works considering localized perturbations, we decompose the semigroup generated by the linearization … Show more
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