算子半群及在火炮管壁温差模型中的应用研究
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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.
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 by
By 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.
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.
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 by
By 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.
引文
[1] E. Hille, Functional Analysis and Semigroups, Amer. Math. Soc. Coll. Publ.,vol.31, Amer. Math. Soc., 1948.
[2] K. Yosida, On the di?erentiability and the representation of one-parametersemigroups of linear operators, J. Math. Soc. Japan, 1948, 1: 15-21.
[3] A. Pazy, Semigroups of Linear Operators and Applications to Partial Di?er-ential Equations, Applied Mathematical Sciences, vol.44, Springer, Berlin,1983.
[4] K.J. Engel, R. Nagel, One-Parameter Semigroups of Linear Evolution Equa-tions, Graduate Texts in Mathematics, vol.194, Springer, Berlin, 2000.
[5] J.K. Hale, Theory of Functional Di?erential Equations, Applied Mathemat-ical Sciences , vol.3, Springer-Verlag, New York, 1977.
[6] J. Wu, Theory and Applications of Partial Functional Di?erential Equations,Applied Mathematical Sciences , vol.119, Springer-Verlag, Berlin, 1996.
[7] Y. Hino, S. Murakami, T. Naito, Functional Di?erential Equations WithUnbounded Delay, Lect. Notes in Math., vol.1473, Springer, Berlin, 1991.
[8] W. Arendt, Vector-valued Laplace transforms and Cauchy problems, IsraelJ. Math., 1987, 59: 327-353.
[9] R. deLaubenfels, Existence Families, Functional Calculi and EvolutionEquations, Lect. Notes in Math., vol.1570, Springer-Verlag, 1994.
[10] W. Arendt, Resolvent pssitive operators and integrated semigroup, Proc.London Math. Soc., 1987, 54(2): 321-349.
[11] H. Kellerman, M. Hieber, Integrated semigroups, J. Funct. Anal., 1989, 84:160-180.
[12] F. Neubrander, Integrated semigroups and their applications to the abstractCauchy problem, Pac. J. Math., 1988, 135: 111-157.
[13] H.R. Thieme, Integrated semigroups and integrated solutions to abstractCauchy problems, J. Math. Anal. Appl., 1990, 152: 416-447.
[14] R. deLaubenfels, Integrated semigroups, C-semigroups and the abstractCauchy problem, Semiproup Forum, 1990, 41: 83-95.
[15] M. Hieber, Integrated semigroups and di?erential operators in Lp spaces,Math. Ann., 1991, 291: 1-16.
[16] Y.C. Li, S.Y. shaw, N-times integrated C-semigroups and the abstractCauchy problems, Taiwanese J. Math., 1997, 1: 75-102.
[17] T.J. Xiao, J. Liang , Approximations of Laplace transforms and integratedsemigroups , J. Funct. Anal., 2000, 172: 202-220.
[18] M. Bachar, W. Desch, Mardiyana, A class of semigroups regularized in spaceand time, J. Math. Anal. Appl., 2006, 314 : 558-578.
[19] M. Mijatovi′c, S. Pilipovi′c, F. Vajzovi′c,α-times integrated semigroups, J.Math. Anal. Appl., 1997, 210: 790-803
[20] R. deLaubenfels, Q. P. Vu?, S. Wang, Laplace transforms of vector-valuedfunctions with growthωand semigroups of operators, Semigroup Forum,2002, 64: 355-375.
[21] R. deLaubenfels, Z. Huang, S. Wang, Y. Wang, Laplace transforms of poly-nomially bounded vecter-valued functions and semigroups of operators, Is-rael J. Math., 1997, 98: 189-207.
[22] Miao Li, Falun Huang, Characterizations of contraction C - semigroup, Proc.Amer. Math. Soc., 1996, 126(4): 1036～1069.
[23] Miao Li, Falun Huang, Quan Zheng, Local integrated C-semigroups, StudiaMath., 2001, 145: 265-280.
[24] Yansong Lei, Wanhua Yi, Quan Zheng, Semigroups of operators and poly-nomials of generators of bounded strongly continuous groups, Proc. LondonMath. Soc., 1994, 69(3): 144-170.
[25] R. Bellman, K. Cooke, Di?erential Di?erence Equations, Academic Press,San Diego, 1963.
[26] M.A. Cruz, J.K. Hale, Asymptotic behavior of neutral functional di?erentialequations, Arch. Rational Mech. Anal., 1969, 34: 331-353.
[27] J.K. Hale, A class of neutral equations with the fixed-point property, Proc.Nat. Acad. Sci. U.S.A., 1970, 67: 136-137.
[28] J.K. Hale, Critical cases for neutral functional di?erential equations, J. Dif-ferential Equations, 1971, 10: 59-82.
[29] J.K. Hale, K.R. Meyer, A class of functional equations of neutral type, Mem.Amer. Math. Soc., 1967, 76.
[30] D. Henry, Linear autonomous neutral functional di?erential equations, J.Di?erential Equations, 1974, 15: 106-128.
[31] R. Datko, Linear autonomous neutral di?erential equations in a Banachspace, J. Di?erential Equations, 1977, 25: 258-274.
[32] C.C. Travis, G.F. Webb, Existence and stability for partial functional dif-ferential equations, Trans. Am. Math. Soc., 1974, 200: 395-418.
[33] G.F. Webb, Autonomous nonlinear functional di?erential equations and non-linear semigroups,J. Math. Anal. Appl., 1974, 46: 1-12.
[34] G. Da Prato, E. Sinestrari, Di?erential operators with non-dense domains,Ann. Scuola Norm. Sup. Pisa Cl. Sci., 1987, 14: 285-344.
[35] M. Adimy, K. Ezzinbi, Strict solutions of nonlinear hyperbolic neutral dif-ferential equations, Appl. Math. Lett.,1999, 12: 107-112.
[36] M. Adimy, K. Ezzinbi, A class of linear partial neutral functional di?erentialequations with nondense domains, Journal of Di?erential Equations, 1998,147: 285-332.
[37] M. Adimy, K. Ezzinbi, Existence and linearized stability for partial neutralfunctional di?erential equations with nondense domains, Di?erential Equa-tions Dynamical Systems, 1999, 7: 371-417.
[38] M. Adimy, K. Ezzinbi, M. Laklach, Existence of solutions for a class ofpartial neutral functional di?erential equations, C. R. Acad. Sci. Paris Ser.IMath., 2000, 330: 957-962.
[39] M. Adimy, K. Ezzinbi, M. Laklach, Spectral decompositon for partial neutralfunctional di?erential equations,Canad. Appl. Math. Quart., 2001, 9: 1-34.
[40] M. Adimy, H. Bouzahir, K. Ezzinbi, Existence and stability for some partialneutral functional di?erential equations with infinite delay, J. Math. Anal.Appl., 2004, 294: 438-461.
[41] M. Adimy, H. Bouzahir, K. Ezzinbi, Existence for a class of partial functionaldi?erential equations with infinite delay, Nonlinear Analysis TMA, 2001,46(1): 91-112.
[42] M. Adimy, H. Bouzahir, K. Ezzinbi, Local existence and stability for somepartial functional di?erential equations with infinite delay, Nonlinear Anal-ysis TMA, 2002, 48(3): 323-348.
[43] K. Ezzinbi, Existence and stability for some partial functional di?eren-tial equations with infinite delay, Electronic J.Di?erential Equations(2003),2003, 116: 1-13.
[44] S. Bochner, A new approach to almost periodicity, Proc. Nat. Acad. Sci.USA., 1962, 48: 2039-2043.
[45] W.A. Veech, Almost automorphic functions on groups, Amer. J. Math.,1965, 87: 719-751.
[46] M. Zaki, Almost automorphic solutions of certain abstract di?erential equa-tions, Annali. di Mat. Pura ed Appl., series 4, 1974, 101: 91-114.
[47] G.M. N’Gu′er′ekata, Topics in Almost Automorphy, Springer-Verlag, NewYork, 2005.
[48] G.M. N’Gu′er′ekata, Almost Automorphic Functions and Almost PeriodicFunctions in Abstract Spaces, Kluwer Academic/Plenum, New York, Lon-don, Moscow, 2001.
[49] J. Liang, J. Zhang, T.J. Xiao, Composition of pseudo almost automorphicand asymptotically almost automorphic functions, J. Math. Anal. Appl.,2008, 340(1): 1493-1499.
[50] T.J. Xiao, J. Liang, J. Zhang, Pseudo almost automorphic solution to semi-linear di?erential equations in Banach spaces, Semigroup Forum, 2008, 76:518-524.
[51] T. Diagana, Existence of p-almost automorphic mild solution to some ab-stract di?erential equations, Int. J. Evol. Equ., 2005, 1(1): 57-67.
[52] J. Liang, G.M. N’Gu′er′ekata, T.J. Xiao, J. Zhang, Some properties of pseudoalmost automorphic functions and applications to abstract di?erential equa-tions, Nonlinear Analysis TMA, 2009,70:2731-2735.
[53] K. Ezzinbi, S. Fatajou, G. M. N’Gu′er′ekata, Pseudo almost automorphicsolutions to some neutral partial functional di?erential equations in Banachspaces, Nonlinear Analysis TMA, 2009, 70:1641-1647.
[54] T.J. Xiao, X.X. Zhu, J. Liang, Pseudo almost automorphic mild solutions tononautonomous di?erential equations and applications. Nonlinear AnalysisTMA, 2009,70:4079-4085.
[55] G.M. N’Gu′er′ekata, A. Pankov, Stepanov-like almost automorphic func-tions and monotone evolution equations, Nonlinear Analysis TMA, 2008,68: 2658-2667.
[56] T. Diagana, G.M. N’Gu′er′ekata, Stepanov-like almost automorphic functionsand applications to some semilinear equations, Applicable Analysis, 2007,86(6): 723-733.
[57] S. Fatajou, N.Van Minh, G.M. N’Gu′er′ekata, A. Pankov, Stepanov-like al-most automorphic solutions for some nonautonomous evolution equations,Electron. J. Di?. Equns., 2007, 121: 1-11.
[58] H. Lee, H. Alkahby, Stepanov-like almost automorphic solutions of nonau-tonomous semilinear evolution equations with delay, Nonlinear Analysis,TMA, 2008, 69: 2158-2166.
[59] T. Diagana, Existence of pseudo almost automorphic solutions to some ab-stract di?erential equations with Sp? Pseudo almost automorphic coe?-cients, Nonlinear Analysis TMA, 2009,70:3781-3790.
[60]蔡睿贤,张娜,柱坐标下变热物性非定常轴对称导热方程的解析解,自然科学进展, 2002, 12(11): 1155-1161.
[61] Shi-chi Chu, Tse-Yung Chang, An analytical solution of transient tempera-ture in a barrel, AD781770.
[62]李小雷,身管弹性问题的理论研究[D],南京理工大学硕士论文,1997.
[63]李小雷,周克栋,苏铁熊,一般轴对称非定常热传导问题的有限元分析,华北工学院学报,1999,20(1): 14-20.
[64]佘建生,薄玉成,杨臻,枪管温度场和热应力的研究,华北工学院学报,2002,23(2): 243-247.
[65] 周克栋,射击时武器身管温度场的分析研究[D ].华东工学院博士论文,1991.
[66] K.C. Jane, Z.Y. Lee, Thermoelastiticity of multilayered cylinders, Journalof Thermal Stress, 1999, 22: 57-74.
[67]田青超,吴建生,樊新民,张越,有限差分法在复合枪管热传中的应用,兵工学报, 2000, 21(4): 297-300.
[68]田青超,樊新民,张越,孔德仁,复合枪管热传的数值分析,南京理工大学学报, 1999, 23(4): 340-343.
[69]陈龙淼,复合材料身管热学性能研究[D],南京理工大学博士论文,2005.
[70]周邦寅,王一平,李立,数学物理方程(第二版),电子工业出版社, 2005.
[71] F.A. Vassallo, C.C. Morphy, Feasibility assessment of conceptual 105-mmM68 comoposite Tubes[R], AD-A177729,1986: 8-15.
[72] T. Diagana , G.M. N’Gu′er′ekata, N.Van Minh, Almost automorphic solutionsof evolution equations, Proc. Amer. Math. Soc., 2004, 132(11): 3289-3298.
[73] I. Cioranescu, Abstract Beurling spaces of class (Mp) and ultradistributionsemigroups, Bull. Sci. Math., 1978, 102:167-192.
[74] S. Mandelbrojt, S′eries adh′erentes, r′egularistion des suites applications,Gauthier-Villars, Paris, 1952.
[75] D. V. Widder, An Introduction to Transform Theory, Acad. Press, NewYork, 1971.
[76] J. Wu, H. Xia, Self-sustained oscillations in a ring array of coupled losslesstransmission lines, J. Di?erential Equations, 1996, 124: 247-278.
[77] J. Wu, H. Xia, Rotating waves in neutral partial functional di?erential equa-tions, J.Dynam.Di?erential Equations, 1999, 1: 209-238.
[78] J.K. Hale, Partial neutral functional di?erential equations, Rev.RoumaineMath. Pures Appl., 1994, 39: 339-344.
[79] J.K. Hale, Coupled oscillators on a circle, Resenhas, 1994, 1(4): 441-457.
[80] T. Naito, J.S. Shin, S. Murakami, The generator of the solution semigroupfor the general linear functional di?erential Equation, Bull.Univ. Electro-Comm., 1998, 11(1): 29-38.
[81] K. Ezzinbi, A. Ouhinou, Necessary and su?cient conditions for the regularityand stability for some partial functional di?erential equations with infinitedelay, Nonlinear Analysis TMA, 2006, 64: 1690-1709.
[82] J. Hale, J. Kato, Phase space for retarded equations with unbounded delay,Funkcia Ekvac, 1978, 21(1):11-41.
[83] R. Benkhalti, K. Ezzinbi, Existence and stability for some partial neutralfunctional di?erential equations, Di?erential and Integral Equations, 2004,17(12):1423-1436.
[84] T. Diagana, G.M. N’Gu′er′ekata, Almost automorphic solutions to someclasses of partial evolution equations, Appl. Math. Lett., 2007, 20(4):462-466.
[85] T. Diagana, Existence and uniqueness of pseudo almost periodic solutions tosome classes of partial evolution equations, Nonlinear Analysis TMA, 2007,66(2):384-395.
[86] A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Prob-lems, Birkh¨auser, Basel, 1995.
[87] R. Johnson, A linear almost periodic equation with an almost automorphicsolution, Proc. Amer. Math. Soc., 1981, 82(2):199-205.
[88] T. Diagana, Existence of pseudo almost periodic solutions to some classesof partial hyperbolic evolution equations, Electron Journal of QualitativeTheory of Di?erential Equations, 2007, 3: 1–12.
[89] Z.R. Hu, Z. Jin, Existence and uniquess of pseudo almost automorphic mildsolutions to some classes of partial hyperbolic evolution equations, DiscreteDynamics in Nature and Society 2008, 2008, 13: doi:10.1155/2008/405092.Article ID 405092.
[90] Z.R. Hu, Z. Jin, Pseudo almost automorphic mild solutions to some classesof partial evolution equations, submitted for publication.
[91] Z.R. Hu, Z. Jin, Pseudo almost automorphic mild solutions to hyperbolicevolution equations with infinite delay in intermediate Banach spaces, sub-mitted for publication.
[92] T. Diagana, C. M. Mahop, G.M. N’Gu′er′ekata, B. Toni, Existence anduniqueness of pseudo almost periodic solutions to some classes of semilineardi?erential equations and applications, Nonlinear Analysis TMA, 2006, 64:2442-2453.
[93] T. Diagana, G.M. N’Gu′er′ekata, Pseudo almost periodic mild solutions tohyperbolic evolution equations in abstract intermediate Banach spaces, Ap-plicable Analysis, 2006, 85(6): 769–780.
[94] T. A. Burton, B. Zhang, Periodic solutions of abstract di?erential equationswith infinite delay, J. Di?erential Equations, 1991, 90: 357-396.
[95] T. Diagana, Pseudo almost periodic solutions to some di?erential equationswith infinite delay, Electron. J. Di?erential Equations 2006, 2006, 79: 1-10.
[96] T. Diagana, Stepanov-like pseudo almost periodicity and its applicationsto some nonautonomous di?erential equations, Nonlinear Analysis TMA,2008,69,4277-4285.
[97] P. Acquistapace, B. Terreni, A unified approach to abstract linear parabolicequations, Rend. Sem. Mat. Univ. Padova, 1987, 78: 47–107.
[98] P. Acquistapace, Evolution operators and strong solution of abstract linearparabolic equations, Di?erential Integral Equations, 1988, 1: 433–457.
[99] L. Maniar, R. Schnaubelt, Almost periodicity of inhomogeneous parabolicevolution equations, in: Lecture Notes in Pure and Appl. Math., Dekker,New York, 2003, 234: 299–318.
[100] H.S. Ding, J. Liang, G.M. N’Gu′er′ekata, T.J. Xiao, Pseudo almost peri-odicity to some nonautonomous evolution equations with delay, NonlinearAnalysis TMA, 2007, 67: 1412-1418.
[101] H.S. Ding, J. Liang G.M. N’Gu′er′ekata, T.J. Xiao, Mild pseudo almostperiodic solutions of nonautonomous semilinear evolution equations, Math-ematical and Computer Modelling, 2007, 45: 579-584.
[102] Z.R. Hu, Z. Jin, Stepanov-like pseudo almost periodic mild solutions toperturbed nonautonomous evolution equations with infinite delay, NonlinearAnalysis TMA, 2009, doi:10.1016/j.na.2009.04.032.
[103] K. Ezzinbi, G.M. N’Gu′er′ekata, Almost automorphic solutions for somepartial functional di?erential equations, J. Math. Anal. Appl., 2007, 328(1):344-358.
[104] S. Boulite, L. Maniar, G.M. N’Gu′er′ekata, Almost automorphic solutionsfor hyperbolic semilinear evolution equations, Semigroup Forum, 2005, 71:231-240.
[105] Y. Hino, S. Murakami, Almost automorphic solutions for abstract func-tional di?erential equations, J. Math. Anal. Appl., 2003, 286(1): 741-752.
[106] G.M. N’Gu′er′ekata, Existence and uniqueness of almost automorphic mildsolutions to some semilinear abstract di?erential equations, Semigroup Fo-rum, 2004, 69: 80-86.
[107] J.A. Goldstein, G.M. N’Gu′er′ekata, Almost automorphic solutions of semi-linear evolution equations, Proc. Amer. Math. Soc., 2005, 133(8): 2401-2408.
[108] N.Van Minh, T. Naito, G.M. N’Gu′er′ekata, A spectral countability condi-tion for almost automorphy of solutions of abstract di?erential equations,Proc. Amer. Math. Soc., 2006, 134(11): 3257-3266.
[109] A. Pankov, Bounded and Almost Periodic Solutions of Nonlinear OperatorDi?erential Equations, Kluwer, Dordrecht, 1990.
[110] C. Chicone, Y. Latushkin, Evolution Semigroups in Dynamical systemsand Di?erential Equations, Proc. Amer. Math. Soc., 1999.
[111] W.A. Coppel, Dichotomies in Stability Theory, Springer-Verlag, 1978.
[112] D. Henry, Geometric Theory of Semilinear Probolic Equations, Springer-Verlag, 1981.
[2] K. Yosida, On the di?erentiability and the representation of one-parametersemigroups of linear operators, J. Math. Soc. Japan, 1948, 1: 15-21.
[3] A. Pazy, Semigroups of Linear Operators and Applications to Partial Di?er-ential Equations, Applied Mathematical Sciences, vol.44, Springer, Berlin,1983.
[4] K.J. Engel, R. Nagel, One-Parameter Semigroups of Linear Evolution Equa-tions, Graduate Texts in Mathematics, vol.194, Springer, Berlin, 2000.
[5] J.K. Hale, Theory of Functional Di?erential Equations, Applied Mathemat-ical Sciences , vol.3, Springer-Verlag, New York, 1977.
[6] J. Wu, Theory and Applications of Partial Functional Di?erential Equations,Applied Mathematical Sciences , vol.119, Springer-Verlag, Berlin, 1996.
[7] Y. Hino, S. Murakami, T. Naito, Functional Di?erential Equations WithUnbounded Delay, Lect. Notes in Math., vol.1473, Springer, Berlin, 1991.
[8] W. Arendt, Vector-valued Laplace transforms and Cauchy problems, IsraelJ. Math., 1987, 59: 327-353.
[9] R. deLaubenfels, Existence Families, Functional Calculi and EvolutionEquations, Lect. Notes in Math., vol.1570, Springer-Verlag, 1994.
[10] W. Arendt, Resolvent pssitive operators and integrated semigroup, Proc.London Math. Soc., 1987, 54(2): 321-349.
[11] H. Kellerman, M. Hieber, Integrated semigroups, J. Funct. Anal., 1989, 84:160-180.
[12] F. Neubrander, Integrated semigroups and their applications to the abstractCauchy problem, Pac. J. Math., 1988, 135: 111-157.
[13] H.R. Thieme, Integrated semigroups and integrated solutions to abstractCauchy problems, J. Math. Anal. Appl., 1990, 152: 416-447.
[14] R. deLaubenfels, Integrated semigroups, C-semigroups and the abstractCauchy problem, Semiproup Forum, 1990, 41: 83-95.
[15] M. Hieber, Integrated semigroups and di?erential operators in Lp spaces,Math. Ann., 1991, 291: 1-16.
[16] Y.C. Li, S.Y. shaw, N-times integrated C-semigroups and the abstractCauchy problems, Taiwanese J. Math., 1997, 1: 75-102.
[17] T.J. Xiao, J. Liang , Approximations of Laplace transforms and integratedsemigroups , J. Funct. Anal., 2000, 172: 202-220.
[18] M. Bachar, W. Desch, Mardiyana, A class of semigroups regularized in spaceand time, J. Math. Anal. Appl., 2006, 314 : 558-578.
[19] M. Mijatovi′c, S. Pilipovi′c, F. Vajzovi′c,α-times integrated semigroups, J.Math. Anal. Appl., 1997, 210: 790-803
[20] R. deLaubenfels, Q. P. Vu?, S. Wang, Laplace transforms of vector-valuedfunctions with growthωand semigroups of operators, Semigroup Forum,2002, 64: 355-375.
[21] R. deLaubenfels, Z. Huang, S. Wang, Y. Wang, Laplace transforms of poly-nomially bounded vecter-valued functions and semigroups of operators, Is-rael J. Math., 1997, 98: 189-207.
[22] Miao Li, Falun Huang, Characterizations of contraction C - semigroup, Proc.Amer. Math. Soc., 1996, 126(4): 1036～1069.
[23] Miao Li, Falun Huang, Quan Zheng, Local integrated C-semigroups, StudiaMath., 2001, 145: 265-280.
[24] Yansong Lei, Wanhua Yi, Quan Zheng, Semigroups of operators and poly-nomials of generators of bounded strongly continuous groups, Proc. LondonMath. Soc., 1994, 69(3): 144-170.
[25] R. Bellman, K. Cooke, Di?erential Di?erence Equations, Academic Press,San Diego, 1963.
[26] M.A. Cruz, J.K. Hale, Asymptotic behavior of neutral functional di?erentialequations, Arch. Rational Mech. Anal., 1969, 34: 331-353.
[27] J.K. Hale, A class of neutral equations with the fixed-point property, Proc.Nat. Acad. Sci. U.S.A., 1970, 67: 136-137.
[28] J.K. Hale, Critical cases for neutral functional di?erential equations, J. Dif-ferential Equations, 1971, 10: 59-82.
[29] J.K. Hale, K.R. Meyer, A class of functional equations of neutral type, Mem.Amer. Math. Soc., 1967, 76.
[30] D. Henry, Linear autonomous neutral functional di?erential equations, J.Di?erential Equations, 1974, 15: 106-128.
[31] R. Datko, Linear autonomous neutral di?erential equations in a Banachspace, J. Di?erential Equations, 1977, 25: 258-274.
[32] C.C. Travis, G.F. Webb, Existence and stability for partial functional dif-ferential equations, Trans. Am. Math. Soc., 1974, 200: 395-418.
[33] G.F. Webb, Autonomous nonlinear functional di?erential equations and non-linear semigroups,J. Math. Anal. Appl., 1974, 46: 1-12.
[34] G. Da Prato, E. Sinestrari, Di?erential operators with non-dense domains,Ann. Scuola Norm. Sup. Pisa Cl. Sci., 1987, 14: 285-344.
[35] M. Adimy, K. Ezzinbi, Strict solutions of nonlinear hyperbolic neutral dif-ferential equations, Appl. Math. Lett.,1999, 12: 107-112.
[36] M. Adimy, K. Ezzinbi, A class of linear partial neutral functional di?erentialequations with nondense domains, Journal of Di?erential Equations, 1998,147: 285-332.
[37] M. Adimy, K. Ezzinbi, Existence and linearized stability for partial neutralfunctional di?erential equations with nondense domains, Di?erential Equa-tions Dynamical Systems, 1999, 7: 371-417.
[38] M. Adimy, K. Ezzinbi, M. Laklach, Existence of solutions for a class ofpartial neutral functional di?erential equations, C. R. Acad. Sci. Paris Ser.IMath., 2000, 330: 957-962.
[39] M. Adimy, K. Ezzinbi, M. Laklach, Spectral decompositon for partial neutralfunctional di?erential equations,Canad. Appl. Math. Quart., 2001, 9: 1-34.
[40] M. Adimy, H. Bouzahir, K. Ezzinbi, Existence and stability for some partialneutral functional di?erential equations with infinite delay, J. Math. Anal.Appl., 2004, 294: 438-461.
[41] M. Adimy, H. Bouzahir, K. Ezzinbi, Existence for a class of partial functionaldi?erential equations with infinite delay, Nonlinear Analysis TMA, 2001,46(1): 91-112.
[42] M. Adimy, H. Bouzahir, K. Ezzinbi, Local existence and stability for somepartial functional di?erential equations with infinite delay, Nonlinear Anal-ysis TMA, 2002, 48(3): 323-348.
[43] K. Ezzinbi, Existence and stability for some partial functional di?eren-tial equations with infinite delay, Electronic J.Di?erential Equations(2003),2003, 116: 1-13.
[44] S. Bochner, A new approach to almost periodicity, Proc. Nat. Acad. Sci.USA., 1962, 48: 2039-2043.
[45] W.A. Veech, Almost automorphic functions on groups, Amer. J. Math.,1965, 87: 719-751.
[46] M. Zaki, Almost automorphic solutions of certain abstract di?erential equa-tions, Annali. di Mat. Pura ed Appl., series 4, 1974, 101: 91-114.
[47] G.M. N’Gu′er′ekata, Topics in Almost Automorphy, Springer-Verlag, NewYork, 2005.
[48] G.M. N’Gu′er′ekata, Almost Automorphic Functions and Almost PeriodicFunctions in Abstract Spaces, Kluwer Academic/Plenum, New York, Lon-don, Moscow, 2001.
[49] J. Liang, J. Zhang, T.J. Xiao, Composition of pseudo almost automorphicand asymptotically almost automorphic functions, J. Math. Anal. Appl.,2008, 340(1): 1493-1499.
[50] T.J. Xiao, J. Liang, J. Zhang, Pseudo almost automorphic solution to semi-linear di?erential equations in Banach spaces, Semigroup Forum, 2008, 76:518-524.
[51] T. Diagana, Existence of p-almost automorphic mild solution to some ab-stract di?erential equations, Int. J. Evol. Equ., 2005, 1(1): 57-67.
[52] J. Liang, G.M. N’Gu′er′ekata, T.J. Xiao, J. Zhang, Some properties of pseudoalmost automorphic functions and applications to abstract di?erential equa-tions, Nonlinear Analysis TMA, 2009,70:2731-2735.
[53] K. Ezzinbi, S. Fatajou, G. M. N’Gu′er′ekata, Pseudo almost automorphicsolutions to some neutral partial functional di?erential equations in Banachspaces, Nonlinear Analysis TMA, 2009, 70:1641-1647.
[54] T.J. Xiao, X.X. Zhu, J. Liang, Pseudo almost automorphic mild solutions tononautonomous di?erential equations and applications. Nonlinear AnalysisTMA, 2009,70:4079-4085.
[55] G.M. N’Gu′er′ekata, A. Pankov, Stepanov-like almost automorphic func-tions and monotone evolution equations, Nonlinear Analysis TMA, 2008,68: 2658-2667.
[56] T. Diagana, G.M. N’Gu′er′ekata, Stepanov-like almost automorphic functionsand applications to some semilinear equations, Applicable Analysis, 2007,86(6): 723-733.
[57] S. Fatajou, N.Van Minh, G.M. N’Gu′er′ekata, A. Pankov, Stepanov-like al-most automorphic solutions for some nonautonomous evolution equations,Electron. J. Di?. Equns., 2007, 121: 1-11.
[58] H. Lee, H. Alkahby, Stepanov-like almost automorphic solutions of nonau-tonomous semilinear evolution equations with delay, Nonlinear Analysis,TMA, 2008, 69: 2158-2166.
[59] T. Diagana, Existence of pseudo almost automorphic solutions to some ab-stract di?erential equations with Sp? Pseudo almost automorphic coe?-cients, Nonlinear Analysis TMA, 2009,70:3781-3790.
[60]蔡睿贤,张娜,柱坐标下变热物性非定常轴对称导热方程的解析解,自然科学进展, 2002, 12(11): 1155-1161.
[61] Shi-chi Chu, Tse-Yung Chang, An analytical solution of transient tempera-ture in a barrel, AD781770.
[62]李小雷,身管弹性问题的理论研究[D],南京理工大学硕士论文,1997.
[63]李小雷,周克栋,苏铁熊,一般轴对称非定常热传导问题的有限元分析,华北工学院学报,1999,20(1): 14-20.
[64]佘建生,薄玉成,杨臻,枪管温度场和热应力的研究,华北工学院学报,2002,23(2): 243-247.
[65] 周克栋,射击时武器身管温度场的分析研究[D ].华东工学院博士论文,1991.
[66] K.C. Jane, Z.Y. Lee, Thermoelastiticity of multilayered cylinders, Journalof Thermal Stress, 1999, 22: 57-74.
[67]田青超,吴建生,樊新民,张越,有限差分法在复合枪管热传中的应用,兵工学报, 2000, 21(4): 297-300.
[68]田青超,樊新民,张越,孔德仁,复合枪管热传的数值分析,南京理工大学学报, 1999, 23(4): 340-343.
[69]陈龙淼,复合材料身管热学性能研究[D],南京理工大学博士论文,2005.
[70]周邦寅,王一平,李立,数学物理方程(第二版),电子工业出版社, 2005.
[71] F.A. Vassallo, C.C. Morphy, Feasibility assessment of conceptual 105-mmM68 comoposite Tubes[R], AD-A177729,1986: 8-15.
[72] T. Diagana , G.M. N’Gu′er′ekata, N.Van Minh, Almost automorphic solutionsof evolution equations, Proc. Amer. Math. Soc., 2004, 132(11): 3289-3298.
[73] I. Cioranescu, Abstract Beurling spaces of class (Mp) and ultradistributionsemigroups, Bull. Sci. Math., 1978, 102:167-192.
[74] S. Mandelbrojt, S′eries adh′erentes, r′egularistion des suites applications,Gauthier-Villars, Paris, 1952.
[75] D. V. Widder, An Introduction to Transform Theory, Acad. Press, NewYork, 1971.
[76] J. Wu, H. Xia, Self-sustained oscillations in a ring array of coupled losslesstransmission lines, J. Di?erential Equations, 1996, 124: 247-278.
[77] J. Wu, H. Xia, Rotating waves in neutral partial functional di?erential equa-tions, J.Dynam.Di?erential Equations, 1999, 1: 209-238.
[78] J.K. Hale, Partial neutral functional di?erential equations, Rev.RoumaineMath. Pures Appl., 1994, 39: 339-344.
[79] J.K. Hale, Coupled oscillators on a circle, Resenhas, 1994, 1(4): 441-457.
[80] T. Naito, J.S. Shin, S. Murakami, The generator of the solution semigroupfor the general linear functional di?erential Equation, Bull.Univ. Electro-Comm., 1998, 11(1): 29-38.
[81] K. Ezzinbi, A. Ouhinou, Necessary and su?cient conditions for the regularityand stability for some partial functional di?erential equations with infinitedelay, Nonlinear Analysis TMA, 2006, 64: 1690-1709.
[82] J. Hale, J. Kato, Phase space for retarded equations with unbounded delay,Funkcia Ekvac, 1978, 21(1):11-41.
[83] R. Benkhalti, K. Ezzinbi, Existence and stability for some partial neutralfunctional di?erential equations, Di?erential and Integral Equations, 2004,17(12):1423-1436.
[84] T. Diagana, G.M. N’Gu′er′ekata, Almost automorphic solutions to someclasses of partial evolution equations, Appl. Math. Lett., 2007, 20(4):462-466.
[85] T. Diagana, Existence and uniqueness of pseudo almost periodic solutions tosome classes of partial evolution equations, Nonlinear Analysis TMA, 2007,66(2):384-395.
[86] A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Prob-lems, Birkh¨auser, Basel, 1995.
[87] R. Johnson, A linear almost periodic equation with an almost automorphicsolution, Proc. Amer. Math. Soc., 1981, 82(2):199-205.
[88] T. Diagana, Existence of pseudo almost periodic solutions to some classesof partial hyperbolic evolution equations, Electron Journal of QualitativeTheory of Di?erential Equations, 2007, 3: 1–12.
[89] Z.R. Hu, Z. Jin, Existence and uniquess of pseudo almost automorphic mildsolutions to some classes of partial hyperbolic evolution equations, DiscreteDynamics in Nature and Society 2008, 2008, 13: doi:10.1155/2008/405092.Article ID 405092.
[90] Z.R. Hu, Z. Jin, Pseudo almost automorphic mild solutions to some classesof partial evolution equations, submitted for publication.
[91] Z.R. Hu, Z. Jin, Pseudo almost automorphic mild solutions to hyperbolicevolution equations with infinite delay in intermediate Banach spaces, sub-mitted for publication.
[92] T. Diagana, C. M. Mahop, G.M. N’Gu′er′ekata, B. Toni, Existence anduniqueness of pseudo almost periodic solutions to some classes of semilineardi?erential equations and applications, Nonlinear Analysis TMA, 2006, 64:2442-2453.
[93] T. Diagana, G.M. N’Gu′er′ekata, Pseudo almost periodic mild solutions tohyperbolic evolution equations in abstract intermediate Banach spaces, Ap-plicable Analysis, 2006, 85(6): 769–780.
[94] T. A. Burton, B. Zhang, Periodic solutions of abstract di?erential equationswith infinite delay, J. Di?erential Equations, 1991, 90: 357-396.
[95] T. Diagana, Pseudo almost periodic solutions to some di?erential equationswith infinite delay, Electron. J. Di?erential Equations 2006, 2006, 79: 1-10.
[96] T. Diagana, Stepanov-like pseudo almost periodicity and its applicationsto some nonautonomous di?erential equations, Nonlinear Analysis TMA,2008,69,4277-4285.
[97] P. Acquistapace, B. Terreni, A unified approach to abstract linear parabolicequations, Rend. Sem. Mat. Univ. Padova, 1987, 78: 47–107.
[98] P. Acquistapace, Evolution operators and strong solution of abstract linearparabolic equations, Di?erential Integral Equations, 1988, 1: 433–457.
[99] L. Maniar, R. Schnaubelt, Almost periodicity of inhomogeneous parabolicevolution equations, in: Lecture Notes in Pure and Appl. Math., Dekker,New York, 2003, 234: 299–318.
[100] H.S. Ding, J. Liang, G.M. N’Gu′er′ekata, T.J. Xiao, Pseudo almost peri-odicity to some nonautonomous evolution equations with delay, NonlinearAnalysis TMA, 2007, 67: 1412-1418.
[101] H.S. Ding, J. Liang G.M. N’Gu′er′ekata, T.J. Xiao, Mild pseudo almostperiodic solutions of nonautonomous semilinear evolution equations, Math-ematical and Computer Modelling, 2007, 45: 579-584.
[102] Z.R. Hu, Z. Jin, Stepanov-like pseudo almost periodic mild solutions toperturbed nonautonomous evolution equations with infinite delay, NonlinearAnalysis TMA, 2009, doi:10.1016/j.na.2009.04.032.
[103] K. Ezzinbi, G.M. N’Gu′er′ekata, Almost automorphic solutions for somepartial functional di?erential equations, J. Math. Anal. Appl., 2007, 328(1):344-358.
[104] S. Boulite, L. Maniar, G.M. N’Gu′er′ekata, Almost automorphic solutionsfor hyperbolic semilinear evolution equations, Semigroup Forum, 2005, 71:231-240.
[105] Y. Hino, S. Murakami, Almost automorphic solutions for abstract func-tional di?erential equations, J. Math. Anal. Appl., 2003, 286(1): 741-752.
[106] G.M. N’Gu′er′ekata, Existence and uniqueness of almost automorphic mildsolutions to some semilinear abstract di?erential equations, Semigroup Fo-rum, 2004, 69: 80-86.
[107] J.A. Goldstein, G.M. N’Gu′er′ekata, Almost automorphic solutions of semi-linear evolution equations, Proc. Amer. Math. Soc., 2005, 133(8): 2401-2408.
[108] N.Van Minh, T. Naito, G.M. N’Gu′er′ekata, A spectral countability condi-tion for almost automorphy of solutions of abstract di?erential equations,Proc. Amer. Math. Soc., 2006, 134(11): 3257-3266.
[109] A. Pankov, Bounded and Almost Periodic Solutions of Nonlinear OperatorDi?erential Equations, Kluwer, Dordrecht, 1990.
[110] C. Chicone, Y. Latushkin, Evolution Semigroups in Dynamical systemsand Di?erential Equations, Proc. Amer. Math. Soc., 1999.
[111] W.A. Coppel, Dichotomies in Stability Theory, Springer-Verlag, 1978.
[112] D. Henry, Geometric Theory of Semilinear Probolic Equations, Springer-Verlag, 1981.