We first determine the dichotomy (Sacker-Sell) spectrum for certain nonautonomous linear evolutionary equations induced by a class of parabolic PDE systems. Having this information at hand. we underline the applicability of our second result: If the widths of the gaps in the dichotomy spectrum are bounded away from $0$. then one can rule out the existence of super-exponentially decayi... https://jalyttlers.shop/product-category/table-cloth/