论文标题
操作员半群的半均匀稳定性和阻尼波的能量衰减
Semi-uniform stability of operator semigroups and energy decay of damped waves
论文作者
论文摘要
只有在过去的十五年左右的时间里，半均匀稳定性的概念就位于指数稳定性和强稳定性之间，才成为$ C_0 $ - 元素的渐近理论的一部分。现在，它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（并且通常是最佳）抽象结果。我们继续指出如何应用这些结果来获得（有时是最佳）能量衰减的速率，以解决某些阻尼的二阶Cauchy问题。
Only in the last fifteen 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 $C_0$-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.
