摘要
研究具一组可修复设备的系统解的适定性和稳定性.使用泛函分析方法,特别是Banach空间上的线性算子理论和C_0半群理论,证明了系统解的适定性以及正解的存在性,证明了系统解的渐近稳定性,指数稳定性以及严格占优本征值的存在性,证实了实际问题中相关假设的合理性.
In this paper, the solution of a series system with repair facility is investigated. By using the method of functional analysis, especially, the linear operator theory and Co semigroup theory on Banach space, the well-posedness of solution and the existence of positive solution are studied. The asymptotic stability and exponential stability of solution are proved and the existence of strictly dominant eigenvalue is showed. The rationality of corresponding hypotheses in practical problem is completely solved.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2007年第4期474-482,共9页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(60473034
60474017)
浙江省自然科学基金(102002)
关键词
可修复设备
适定性
G半群
耗散算子
渐近稳定性
严格占优本征值
指数
稳定性
repair facility
well-posedness
Co semigroup
dissipative operator
asymptotic stability
strictly dominant eigenvalue
exponential stability
