具一组可修复设备的系统解的适定性和稳定性  

Well-posedness and stability of solution of a series system with repair facility

作　　者：汪文珑[1] 许跟起[2] 

机构地区：[1]绍兴文理学院数学系,浙江绍兴312000 [2]天津大学数学系,天津300072

出　　处：《高校应用数学学报（A辑）》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)

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.

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 

分 类 号：O174.21[理学—数学]