幾類演化型算子的多項式漸近行為研究
發(fā)布時間：2018-12-18 10:57
【摘要】：論文的第一章首先綜述了演化型算子漸近性行為的發(fā)展背景意義以及已經(jīng)獲得的研究成果。在第二章中給出了 Banach空間中離散時間系統(tǒng)有關(guān)多項式穩(wěn)定的四種定義,并借助實例闡釋了四者之間的關(guān)系,運用研究指數(shù)型穩(wěn)定性的方法,我們探討了多項式穩(wěn)定的離散特征,并得到了指數(shù)穩(wěn)定理論中一些經(jīng)典結(jié)論在在多項式穩(wěn)定情況下的變形。第三章主要給出了 Banach 空間上斜演化半流的弱多項式膨脹的概念,討論了定義之間的相互聯(lián)系并對其積分條件進(jìn)行討論,得到了一些滿足弱多項式膨脹性的充要條件。在應(yīng)用方面,利用定義的Lyapunov函數(shù)來研究了一些相應(yīng)概念的積分特征。第四章給出了滿足實線上演化族關(guān)于對(Lp(R,X),Lq(R,X))的多項式三分性的一些充分必要條件。在這里我們討論了對(Lp(R,X),Lq(R,X))的容許性與演化族的一致多項式三分性的關(guān)系。并給出了實例來證明這一點。在文章的最后,我們對本文進(jìn)行了總結(jié)并對一些可以繼續(xù)研究的問題進(jìn)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.
【學(xué)位授予單位】：中國礦業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O177
本文編號：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.
【學(xué)位授予單位】：中國礦業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O177
【參考文獻(xiàn)】
相關(guān)期刊論文 前3條
1 岳田;雷國梁;宋曉秋;;巴拿赫空間中演化算子的非一致多項式膨脹性[J];數(shù)學(xué)的實踐與認(rèn)識;2015年18期
2 岳田;宋曉秋;雷國梁;;線性離散時間系統(tǒng)的非一致多項式膨脹性[J];應(yīng)用泛函分析學(xué)報;2015年03期
3 李志剛;宋曉秋;岳田;;巴拿赫空間上發(fā)展算子的非一致多項式三分性[J];山東大學(xué)學(xué)報(理學(xué)版);2013年12期
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