n次积分C半群与抽象Cauchy问题的指数稳定性

n-Times Integrated C-Semigroups and Exponential Stability of an Abstract Cauchy Problem

基于n次积分C半群的概念和性质,利用泛函分析方法和算子理论讨论了Hilbert空间中n次积分C半群的相应抽象Cauchy问题的指数稳定性,并给出了判断其指数稳定的充要条件,从而将强连续半群的指数稳定性理论中的一些经典结论推广到了n次积分C半群.

Based on the concept and properties of n -times integrated C-semigroups, exponential stability of its relevant abstract Cauchy problem is discussed in the light of functional analysis methods and operator theories in Hilbert space, and the necessary and sufficient conditions concerning the exponential stability are given. The well- konwn results for exponential stability of strongly continuous semigroups are extended to the case of n- times integrated C- semigroups.