Only in the last 15 years or so has the notion of semi-uniform stability, which lies between exponential stability and strong stability, become part of the asymptotic theory of C0-semigroups. It now lies at the very heart of modern semigroup theory. After briefly reviewing the notions of exponential and strong stability, we present an overview of some of the best known (and often optimal) abstract results on semi-uniform stability. We go on to indicate briefly how these results can be applied to obtain (sometimes optimal) rates of energy decay for certain damped second-order Cauchy problems. This article is part of the theme issue ‘Semigroup applications everywhere’.

中文翻译：

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算子半群的半均匀稳定性与阻尼波的能量衰减

直到最近15年左右，介于指数稳定性和强稳定性之间的半均匀稳定性的概念才成为C0-半群渐近理论的一部分。它现在是现代半群理论的核心。在简要回顾了指数稳定性和强稳定性的概念之后，我们概述了一些关于半均匀稳定性的最著名（通常是最佳）抽象结果。我们继续简要说明如何应用这些结果来获得（有时是最佳的）某些阻尼二阶柯西问题的能量衰减率。这篇文章是主题问题“无处不在的半组应用程序”的一部分。