完全二阶抽象Cauchy问题的C-适定性及其应用

在本文中,我们给出了算子矩阵生成指数有界的半群的充分必要条件,其中A0,A1为完全二阶抽象柯西问题（ACP2）的系数算子,并讨论了它与（ACP2）在某种意义下的C-适定性之间的关系．最后,我们应用此结果及［3］中的结论讨论了一类具有应用背景的完全二阶抽象柯西问题的C-适定性．     

Fréchet空间中的二阶线性微分方程Cauchy问题的适定性

在本文中,我们讨论了 Fréchet 空间中二阶线性微分方程 Cauchy 问题的适定性,得到了一个 Hille-Yosida 型结果.     

α-次积分C-半群与抽象柯西问题

本文引入一般的α-次积分C-半群和mildα-次积分C-存在族概念,并讨论它们与抽象柯西问题的联系．     

向量值柯西问题的适定性

设A为复Banach空间X上的稠定闭算子.我们证明了若抽象柯西问题具有C-适定性,则{λ∈C:Reλ≥0）　ρ（A）且存在C>0,使得任给λ∈C,Reλ≥0,都有（λ-A）-1≤C/1+　λ.因而A必为X上某一有界解析半群的无穷小生成元.对于定义在有限区间[0,T]上的抽象柯西问题,我们亦得到了类似的结果.     

系统科学与数学第21卷2001年总目次

第１期σ－Ｃ＊－代数中的正映射………………………………………许天周（１）回归函数核估计的随机加权法……………………………… 薛留根 胡玉萍（９）带两类服务的一般休假 Ｍ／ＧＩ／１型系统的随机分解………………………… 朱翼隽（２３）完全二阶抽象柯西问题的温和Ｃ－存在族和解空间…………………………高明杵（３３）平面自治系统同宿轨族的存在唯一性……………………………………杨启贵（３９）微分代数系统的渐近性…………………………… 陈伯山 廖晓昕 刘永清（４８）求解单调变分不等式问题的一个连续型迭代方法……………     

Fréchet空间中的二阶线性微分方程Cauchy问题的适定性

在本文中,我们讨论了 Fréchet 空间中二阶线性微分方程 Cauchy 问题的适定性,得到了一个 Hille-Yosida 型结果.     

Banach空间二阶脉冲积微分方程终值问题

利用上下解方法讨论了抽象空间中定义在无穷区间上且有无穷个脉冲点的一类二阶脉冲积微分方程终值问题,获得了其最小最大解的存在性.     

Gevrey空间中抽象柯西-柯瓦列夫斯卡娅定理:能量方法

本文研究了非线性柯西问题的适定性问题.利用经典的能量法和抽象柯西-柯瓦列夫斯卡娅定理,得到非线性柯西问题在Gevrey空间中是适定的.推广了已有文献在非线性柯西问题适定性方面的研究.     

带势的非线性Klein-Gordon方程柯西问题的稳定和不稳定集

对带势的非线性Klein-Gordon方程柯西问题,我们定义了新的对于初值的稳定和不稳定集.我们证明了如果发展进入了不稳定集,解在有限时间内爆破;如果发展进入了稳定集,解整体存在.运用势并讨论,我们回答了当初值为多少时,柯西问题的整体解存在.     

带竞争势的非线性Klein-Gordon方程的稳定集和不稳定集

收稿研究带竞争势的非线性Klein-Gordon方程的柯西问题.首先定义了新的稳定集和不稳定集.其次证明了如果初值进入不稳定集,该柯西问题的解在有限时间内爆破;如果初值进入稳定集,该柯西问题的整体解存在.最后运用势井讨论,我们回答了当初值在什么范围时,该柯西问题的整体解存在这个问题.     

Mild Integrated C-existence Families and Abstract Cauchy Problems

in this paper, we first give a Hille-Yosida type sufficient and necessary conditionfor n-times integrated mild C-existence families. Then, we present a Laplace type sufficientand necessary condition for exponentially bounded n-times integrated C-semigrougs, andstudy the relationship between integrated regularized semigroups and general regularizedsemigroups. Finally, we offer a characterization of integrated C-semigroups in terms of thesolvability of abstract Cauchy problems.     

HOLOMORPHIC INTERGATED MILD C-EXISTENCE FAMILIES

0IntroductionIn[1],deLaubenfelsdefilledexpollelltiitllyboullded11olonlorphicC-existeuccfalllilies,holomorpllicC-senhgroupsand11olonlorpllicilltegratedselnigroups.Healsodiscussedtheirrelationships,alldgavesomeHille-YOsidatypecollditiollsforalloperatortogenerateallyofthesefamiliesofoperatorsin[1].ZllengalldLetdefinedexpollelltiallyboulldedllololllorphiconceilltegratedC-semigroups,andpreselltedageueratiolltlleorelllill[2J.Moregelleral71-tilllesintegratedmildC-existencefamilieswereintroducedby…     

α次积分C—存在族与抽象Cauchy问题

本我们讨论弱α次积分C－存在族、α次积分C－存在族、强α次积分C－存在族及其对抽象Cauchy问题的应用。     

Algebra homomorphisms defined via convoluted semigroups and cosine functions

Transform methods are used to establish algebra homomorphisms related to convoluted semigroups and convoluted cosine functions. Such families are now basic in the study of the abstract Cauchy problem. The framework they provide is flexible enough to encompass most of the concepts used up to now to treat Cauchy problems of the first- and second-order in general Banach spaces. Starting with the study of the classical Laplace convolution and a cosine convolution, along with associated dual transforms, natural algebra homomorphisms are introduced which capture the convoluted semigroup and cosine function properties. These correspond to extensions of the Cauchy functional equation for semigroups and the abstract d'Alembert equation for the case of cosine operator functions. The algebra homomorphisms obtained provide a way to prove Hille-Yosida type generation theorems for the operator families under consideration.     

解一类抽象积—微分方程的积分半群方法

在这篇文章内，研究一类含参数线性一算子族Ａ（ｔ）和线性算子Ｂ的积－微分方程，应用积分半群方法证明了该方程存在指数有界解，和含Ａ（ｔ），Ｂ的二阶微分方程存在指数有界和分解。这里Ａ（ｔ），Ｂ不必满足Ｈｉｌｌｅ－Ｙｏｓｉｄａ条件。     

Hille-Yosida operators and Cauchy problems

A new proof of a temporal regularity result for an abstract Cauchy problem with a Hille-Yosida operator is given having consequences on the existence of other types of solutions. New types of weak solutions are introduced.     

Cauchy problem of semi-linear parabolic equations with weak data in homogeneous space and application to the Navier-Stokes equations

In this paper we study the Cauchy problem for a class of semi-linear parabolic type equations withweak data n the homogeneous spaces.We give a method which can be used to construct local mild solutionsof the abstract Cauchy problem in C(σ,s,p)and L~q([O,T);H~(s,p)by introducing the concept of both admissiblequintuptet and compatible space and establishing estblishing time-space estimates for solutions to the linear parabolic typeequations For the small data,we prove that these results can be extended globally in time. We also study the     

Regularized semigroups of bounded semivariation

We use regularized semigroups to consider local linear and semilinear inhomogeneous abstract Cauchy problems on a Banach space in a unified way. We show that the inhomogeneous abstract Cauchy problem {fx43-1} has a unique classical solution, for allf εC([0,T], [Im(C)]),x inC(D(A)), if and only ifA generates aC-regularized semigroup of bounded semivariation, and has a strong solution for allf εL ¹ ([0,T], [Im(C)]),x εC(D(A)) if and only if theC-regularized semigroup is what we call of bounded super semivariation. This includes locally Lipschitz continuousC-regularized semigroups. We give similar simple sufficient conditions for the semilinear abstract Cauchy problem {fx43-2} to have a unique solution. Well-known results for generators of strongly continuous semigroups, as well as more recent results for Hille-Yosida operators, originally due to Da Prato and Sinestrari, regarding (0.1), are immediate corollaries of our results. Results due to Desch, Schappacher and Zhang, on (0.2), for generators of strongly continuous semigroups, are similarly generalized to Hille-Yosida operators with our approach. This article appeared in the last issue of the Forum. However, due to an error by the Journal Secetary, the Abstract was omitted, and with it the equations which are the focus of the article. We therefore are reprinting the article in its entirety. The Journal Secretary regrets the error.