【作者】 胡占荣；

【导师】 靳祯；

【作者基本信息】 中北大学 ， 火炮、自动武器与弹药工程， 2009， 博士

【摘要】 本文主要研究算子半群理论及其在中立型偏泛函微分方程与发展方程中的某些应用.同时,本文还应用算子半群与偏微分方程理论研究了火炮身管固壁温差模型.全文共分十章.第一章介绍了本文的研究背景、研究方法、研究内容与研究结果.第二章是预备知识.主要包括强连续半群、积分半群与拟概自守函数的定义与基本性质.第三章引入关于ω(t)有界向量值函数的n次积分Laplace变换概念,并研究了它的性质.基于这些性质,第三章还建立了关于ω(t)有界的n次积分半群的Hille–Yosida定理.第四章以积分半群为工具研究了下列有限时滞中立型泛函微分方程:得到了其积分解成为严格解的充要条件,其中A : D(A)→X是Banach空间X上的Hille–Yosida算子, L是从CX = C([?r,0],X)到X的有界线性算子,且R(L) ? D(A) , F是从CX到X的非线性连续算子.对t≥0, xt : [?r,0]→X定义为第五章以积分半群为工具研究了下列无限时滞中立型泛函微分方程解的正则性与稳定性:得到了这类方程积分解成为严格解的充要条件,以及解半群稳定的充分条件,其中A : D(A)→X是Banach空间X上的Hille–Yosida算子, B是一个从(?∞,0]到X的函数空间,满足一些公理, F和G是从B到X的非线性连续第六章以强连续半群为工具建立了下列发展方程在Banach空间X上的拟概自守温和解存在唯一的充分条件:其中A是Banach空间X上的指数稳定强连续半群的无穷小生成元, B,C是X上的稠定线性算子, f,g : R×X→X是拟概自守函数.第七章以解析半群为工具建立了下列发展方程在内插Banach空间Xα上的拟概自守温和解存在唯一的充分条件:其中A是Banach空间X上的扇形算子,σ(A)∩iR = ?, B,C是Xα上的有界线性算子,f,g是拟概自守函数.第八章以发展族为工具建立了下列带Stepanov拟概自守项的非自治发展方程拟概自守温和解的存在唯一性定理:其中, A(t)满足“Acquistapace?Terreni”条件, A(t)生成的发展族(U(t,s))t≥s具有指数二分性,格林函数Γ(t,s)双自守, B,C(t,s)t≥s是有界线性算子, h, f,F是连续的Stepanov拟概自守函数(p > 1).第九章结合算子半群与微分方程理论研究了火炮身管固壁温差模型,得到了复合材料身管固壁传热控制微分方程的解析解.第十章对全文进行了总结.更多还原

【Abstract】 This thesis is devoted to investigating mainly semigroups of operators andsome applications to neutral partial functional di?erential equations and evo-lution equations. Also, combining with theory of semigroups of operators andpartial di?erential equations, the model of temperature field in artillery barrelwall is studied. This thesis consists of ten chapters.The first chapter introduces the research background, methods, contents andresults of this thesis.Chapter 2 is preliminaries, mainly including some definitions and basic prop-erties on strongly continuous semigroups, integrated semigroups and pseudo al-most automorphic functions.Chapter 3 introduces the concept and characterizes the properties of n-timesintegrated Laplace transforms of O(ω(t)) vector-valued functions. Based on theseproperties, chapter 3 establishes Hille-Yosida type theorems for O(ω(t)) n-timesintegrated semigroups.With the help of integrated semigroups, chapter 4 investigates the regularityof solutions for the following partial neutral functional di?erential equations withfinite delay ?and obtains the su?cient and necessary conditions for its integral solution tobecome strict solution, where A : D(A)→X is a nondensely defined Hille-Yosida operator, L is a bounded linear operator from CX = C([?r,0],X) to Xsuch that R(L) ? D(A) , F is a nonlinear continuous operator from CX to X.For t≥0, xt : [?r,0]→X is defined as Using integrated semigroups, in chapter 5 we investigate the regularity andstability of solutions for the following partial neutral functional di?erential equa-tions with infinite delayand obtain the su?cient and necessary conditions for its integral solution tobecome strict solution, and the necessary conditions for its solution semigroupto be stable, where A is a nondensely defined Hille-Yosida operator on a Banachspace X endowed with the norm·, B is a seminormed linear space of functionsmapping (?∞,0] to X and satisfies some fundamental axioms, F and G arenonlinear continuous operators from B to X. For every t≥0, xt is a functionmapping (?∞,0] into X which is defined byBy means of strongly continuous semigroups, chapter 6 establishes su?cientconditions for the existence and uniqueness of pseudo almost automorphic mildsolutions to evolution equationwhere A is the infinitesimal generator of exponentially stable strongly continuoussemigroups T(t)t≥0 on a Banach space X, B,C are bounded linear operators onX, f : R×X→X, g : R×X→X are pseudo almost automorphic.Chapter 7 obtains su?cient conditions for the existence and uniqueness ofpseudo almost automorphic mild solutions to evolution equationwhere A is a sectorial linear operator on a Banach space X andσ(A)∩iR = ?,B,C are bounded linear operators on Xα, f : R×X→Xβ, g : R×X→X arepseudo almost automorphic. Chapter 8 aims to establish the existence and uniqueness theorems of pseudoalmost automorphic mild solutions to the following nonautonomous evolutionequations with Stepanov-like pseudo almost automorphic termswhere A(t) satisfy“Acquistapace?Terreni”conditions, evolution family (U(t,s))t≥sgenerated by A(t) has exponential dichotomy, Green’s functionΓ(t,s) is bi-almostautomorphic, B,C(t,s)t≥s are bounded linear operators, h, f, F are Stepanov-like pseudo almost automorphic for p > 1 and continuous.Combining with theory of semigroups of operators and di?erential equations,chapter 9 is on the model of temperature field of artillery barrel wall, obtainingthe analytic solutions to the heat-controlled di?erential equations of compositematerial barrel wall.Chapter 10 is devoted to summing up the whole thesis.更多还原