几类演化型算子的多项式渐近行为研究
发布时间：2018-12-18 10:57
【摘要】：论文的第一章首先综述了演化型算子渐近性行为的发展背景意义以及已经获得的研究成果。在第二章中给出了 Banach空间中离散时间系统有关多项式稳定的四种定义,并借助实例阐释了四者之间的关系,运用研究指数型稳定性的方法,我们探讨了多项式稳定的离散特征,并得到了指数稳定理论中一些经典结论在在多项式稳定情况下的变形。第三章主要给出了 Banach 空间上斜演化半流的弱多项式膨胀的概念,讨论了定义之间的相互联系并对其积分条件进行讨论,得到了一些满足弱多项式膨胀性的充要条件。在应用方面,利用定义的Lyapunov函数来研究了一些相应概念的积分特征。第四章给出了满足实线上演化族关于对(Lp(R,X),Lq(R,X))的多项式三分性的一些充分必要条件。在这里我们讨论了对(Lp(R,X),Lq(R,X))的容许性与演化族的一致多项式三分性的关系。并给出了实例来证明这一点。在文章的最后,我们对本文进行了总结并对一些可以继续研究的问题进行了展望。
[Abstract]:In the first chapter, the development background and research results of asymptotic behavior of evolutional operators are reviewed. In the second chapter, four definitions of polynomial stability for discrete time systems in Banach space are given, and the relationship between the four is explained by an example. By using the method of studying exponential stability, we discuss the discrete characteristics of polynomial stability. The deformation of some classical conclusions in exponential stability theory is obtained under the condition of polynomial stability. In chapter 3, we give the concept of weak polynomial expansion of oblique evolution half-flow in Banach space, discuss the interrelation between definitions and discuss its integral conditions, and obtain some necessary and sufficient conditions to satisfy the expansion of weak polynomial. In the aspect of application, the integral characteristics of some corresponding concepts are studied by using the defined Lyapunov function. In chapter 4, we give some necessary and sufficient conditions for the polynomials of the evolution family on the real line to satisfy the (Lp (Rnx X), Lq (RX). In this paper, we discuss the relation between the admissibility of (Lp (RNX X), Lq (RX) and the trichotomies of uniform polynomials of evolutionary families. An example is given to prove this point. At the end of the paper, we summarize this paper and look forward to some problems we can continue to study.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177
本文编号：2385745
[Abstract]:In the first chapter, the development background and research results of asymptotic behavior of evolutional operators are reviewed. In the second chapter, four definitions of polynomial stability for discrete time systems in Banach space are given, and the relationship between the four is explained by an example. By using the method of studying exponential stability, we discuss the discrete characteristics of polynomial stability. The deformation of some classical conclusions in exponential stability theory is obtained under the condition of polynomial stability. In chapter 3, we give the concept of weak polynomial expansion of oblique evolution half-flow in Banach space, discuss the interrelation between definitions and discuss its integral conditions, and obtain some necessary and sufficient conditions to satisfy the expansion of weak polynomial. In the aspect of application, the integral characteristics of some corresponding concepts are studied by using the defined Lyapunov function. In chapter 4, we give some necessary and sufficient conditions for the polynomials of the evolution family on the real line to satisfy the (Lp (Rnx X), Lq (RX). In this paper, we discuss the relation between the admissibility of (Lp (RNX X), Lq (RX) and the trichotomies of uniform polynomials of evolutionary families. An example is given to prove this point. At the end of the paper, we summarize this paper and look forward to some problems we can continue to study.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177
【参考文献】
相关期刊论文 前3条
1 岳田;雷国梁;宋晓秋;;巴拿赫空间中演化算子的非一致多项式膨胀性[J];数学的实践与认识;2015年18期
2 岳田;宋晓秋;雷国梁;;线性离散时间系统的非一致多项式膨胀性[J];应用泛函分析学报;2015年03期
3 李志刚;宋晓秋;岳田;;巴拿赫空间上发展算子的非一致多项式三分性[J];山东大学学报(理学版);2013年12期
，本文编号：2385745
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