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Only in the last fifteen years or so has the notion of semi-uniformstability, which lies between exponential stability and strong stability,become part of the asymptotic theory of $C_0$-semigroups. It now lies at thevery heart of modern semigroup theory. After briefly reviewing the notions ofexponential and strong stability, we present an overview of some of the bestknown (and often optimal) abstract results on semi-uniform stability. We go onto indicate briefly how these results can be applied to obtain (sometimesoptimal) rates of energy decay for certain damped second-order Cauchy problems.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Semi-uniform stability of operator semigroups and energy decay of damped waves