Exact Boundary Controllability for a Kind of Second-Order Quasilinear Hyperbolic Systems 被引量：6

Exact Boundary Controllability for a Kind of Second-Order Quasilinear Hyperbolic Systems

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摘要 Based on the theory of semi-global C 1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems,the local exact boundary controllability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.

作者 Ke WANG

机构地区 School of Mathematical Sciences

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2011年第6期803-822,共20页 数学年刊（B辑英文版）

基金 supported by the Excellent Doctoral Research Foundation for Key Subject of Fudan University (No.EHH1411208)

关键词 First-order quasilinear hyperbolic systems Second-order quasilinearhyperbolic systems Exact boundary controllability Mixed initial-boundary value problem 拟线性双曲系统边界二阶可控一阶

分类号 O175.27 [理学—数学] O175.1 [理学—基础数学]

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相关文献

参考文献5

1Tatsien LI,Bopeng RAO.Strong (Weak) Exact Controllability and Strong (Weak) Exact Observability for Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2010,31(5):723-742. 被引量：12
2LI TA-TSIEN (LI DAQIAN), JIN YI Department of Mathematics, Fudan University, Shanghai 200433, China..SEMI-GLOBAL C^1 SOLUTION TO THE MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Chinese Annals of Mathematics,Series B,2001,22(3):325-336. 被引量：31
3ＬＩＴＡ－ＴＳＩＥＮ,ＲＡＯ ВＯＰＥＮＧ.ＬＯＣＡＬＥＸＡＣＴＢＯＵＮＤＡＲＹＣＯＮＴＲＯＬＬＡＢＩＬＩＴＹＦＯＲＡＣＬＡＳＳＯＦＱＵＡＳＩＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＳＹＳＴＥＭＳ[J].Chinese Annals of Mathematics,Series B,2002,23(2):209-218. 被引量：30
4于立新.二阶拟线性双曲型方程组的精确边界能控性(英文)[J].工程数学学报,2005,22(2):199-211. 被引量：4
5庄凯丽,尚培培.二阶拟线性双曲型方程的精确边界能控性[J].工程数学学报,2009,26(6):1005-1020. 被引量：3

二级参考文献12

1Zhiqiang WANG.Exact Controllability for Nonautonomous First Order Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2006,27(6):643-656. 被引量：13
2Li Tatsien，C R Acad Sci Paris Ser 1，2000年，205页被引量：1
3Li Tatisen，M2AN，2000年，34卷，399页被引量：1
4Li Tatsien，J Math Anal Appl，1998年，225卷，289页被引量：1
5Li Tatsien，Commun Part Diff Eqs，1994年，19卷，1263页被引量：1
6Li Tatsien，Research in Applied Mathematics.32，1994年被引量：1
7Li Tatsien，Duke University Mathematics Series V，1985年被引量：1
8Li Tatsien，Chin Ann Math B，1981年，2卷，65页被引量：1
9尚培培,庄凯丽.二阶拟线性双曲型方程的精确能观性[J].工程数学学报,2009,26(4):618-636. 被引量：3
10ＬＩＴＡ－ＴＳＩＥＮ,ＲＡＯ ВＯＰＥＮＧ.ＬＯＣＡＬＥＸＡＣＴＢＯＵＮＤＡＲＹＣＯＮＴＲＯＬＬＡＢＩＬＩＴＹＦＯＲＡＣＬＡＳＳＯＦＱＵＡＳＩＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＳＹＳＴＥＭＳ[J].Chinese Annals of Mathematics,Series B,2002,23(2):209-218. 被引量：30

共引文献43

1王珂,石志娟.一维线性波动方程耦合组的精确边界同步能观性[J].数学年刊（A辑）,2020(2):139-152.
2王志强,于立新.一维绝热流方程组的精确边界能控性[J].高校应用数学学报（A辑）,2008,23(1):35-40. 被引量：1
3于勇.河渠非定常流的精确边界能控性[J].高校应用数学学报（A辑）,2004,19(4):379-393. 被引量：1
4于立新.二阶拟线性双曲型方程组的精确边界能控性(英文)[J].工程数学学报,2005,22(2):199-211. 被引量：4
5YuLixin.EXACT BOUNDARY CONTROLLABILITY FOR HIGHER ORDER QUASILINEAR HYPERBOLIC EQUATIONS[J].Applied Mathematics(A Journal of Chinese Universities),2005,20(2):127-141. 被引量：2
6李大潜.拟线性双曲型方程(组)的精确能控性[J].高校应用数学学报（A辑）,2005,20(2):127-146. 被引量：2
7徐玉兰.拟线性双曲组一类非局部混合初-边值问题的半整体C^1解[J].高校应用数学学报（A辑）,2006,21(1):49-60. 被引量：1
8Zhiqiang WANG.Exact Controllability for Nonautonomous First Order Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2006,27(6):643-656. 被引量：13
9叶莎莎.一阶半线性双曲型方程组的精确边界能控性与能观性[J].工程数学学报,2007,24(5):864-878.
10张祺.拟线性双曲型方程组具较少控制函数的双侧精确边界能控性[J].高校应用数学学报（A辑）,2009(1):65-74.

同被引文献10

1于立新.二阶拟线性双曲型方程组的精确边界能控性(英文)[J].工程数学学报,2005,22(2):199-211. 被引量：4
2Zhiqiang WANG.Exact Controllability for Nonautonomous First Order Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2006,27(6):643-656. 被引量：13
3尚培培,庄凯丽.二阶拟线性双曲型方程的精确能观性[J].工程数学学报,2009,26(4):618-636. 被引量：3
4庄凯丽,尚培培.二阶拟线性双曲型方程的精确边界能控性[J].工程数学学报,2009,26(6):1005-1020. 被引量：3
5Tatsien LI,Bopeng RAO.Strong (Weak) Exact Controllability and Strong (Weak) Exact Observability for Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2010,31(5):723-742. 被引量：12
6Gnter R.LEUGERING,E.J.P.Georg SCHMIDT.On Exact Controllability of Networks of Nonlinear Elastic Strings in 3-Dimensional Space[J].Chinese Annals of Mathematics,Series B,2012,33(1):33-60. 被引量：1
7Long HU,Fanqiong JI,Ke WANG.Exact Boundary Controllability and Exact Boundary Observability for a Coupled System of Quasilinear Wave Equations[J].Chinese Annals of Mathematics,Series B,2013,34(4):479-490. 被引量：4
8Ke WANG.Exact Boundary Observability for a Kind of Second-Order Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2016,37(6):803-820. 被引量：2
9ＬＩＴＡ－ＴＳＩＥＮ,ＲＡＯ ВＯＰＥＮＧ.ＬＯＣＡＬＥＸＡＣＴＢＯＵＮＤＡＲＹＣＯＮＴＲＯＬＬＡＢＩＬＩＴＹＦＯＲＡＣＬＡＳＳＯＦＱＵＡＳＩＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＳＹＳＴＥＭＳ[J].Chinese Annals of Mathematics,Series B,2002,23(2):209-218. 被引量：30
10LI TA-TSIEN (LI DAQIAN), JIN YI Department of Mathematics, Fudan University, Shanghai 200433, China..SEMI-GLOBAL C^1 SOLUTION TO THE MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Chinese Annals of Mathematics,Series B,2001,22(3):325-336. 被引量：31

引证文献6

1Tatsien LI,Bopeng RAO.Exact Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls[J].Chinese Annals of Mathematics,Series B,2013,34(1):139-160. 被引量：14
2Long HU,Fanqiong JI,Ke WANG.Exact Boundary Controllability and Exact Boundary Observability for a Coupled System of Quasilinear Wave Equations[J].Chinese Annals of Mathematics,Series B,2013,34(4):479-490. 被引量：4
3Ke WANG.Exact Boundary Observability for a Kind of Second-Order Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2016,37(6):803-820. 被引量：2
4Qilong GU,Günter LEUGERING,Tatsien LI.Exact Boundary Controllability on a Tree-Like Network of Nonlinear Planar Timoshenko Beams[J].Chinese Annals of Mathematics,Series B,2017,38(3):711-740.
5史琨,于立新.星状河渠网络中非稳定流的精确边界能控性[J].烟台大学学报（自然科学与工程版）,2022,35(2):134-141.
6王珂,潘盼盼.一个一维二阶拟线性双曲组的精确边界能控性[J].Chinese Quarterly Journal of Mathematics,2023,38(4):424-440.

二级引证文献16

1王珂,石志娟.一维线性波动方程耦合组的精确边界同步能观性[J].数学年刊（A辑）,2020(2):139-152.
2王晨牧.一类波动方程耦合系统具Dirichlet边界控制的部分精确边界同步性[J].数学年刊（A辑）,2020(2):115-138. 被引量：1
3Xing LU.Local Exact Boundary Synchronization for a Kind of First Order Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2019,40(1):79-96.
4LI TaTsien.From phenomena of synchronization to exact synchronization and approximate synchronization for hyperbolic systems[J].Science China Mathematics,2016,59(1):1-18. 被引量：3
5Ke WANG.Exact Boundary Observability for a Kind of Second-Order Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2016,37(6):803-820. 被引量：2
6Tatsien LI,Bopeng RAO.Exact Boundary Controllability for a Coupled System of Wave Equations with Neumann Boundary Controls(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)[J].Chinese Annals of Mathematics,Series B,2017,38(2):473-488. 被引量：3
7吴克凡.常微分系统同步的控制理论（英文）[J].数学杂志,2019,39(3):357-369.
8WANG Yan-yan.Induced generalized exact boundary synchronizations for a coupled system of wave equations[J].Applied Mathematics(A Journal of Chinese Universities),2020,35(1):113-126.
9Yanyan WANG.Determination of generalized exact boundary synchronization matrix for a coupled system of wave equations[J].Frontiers of Mathematics in China,2019,14(6):1339-1352.
10Yanyan WANG.Generalized Exact Boundary Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls[J].Chinese Annals of Mathematics,Series B,2020,41(4):511-530.

1李书敏.CAUCHY PROBLEM FOR GENERAL FIRST ORDER INHOMOGENEOUS QUASILINEAR HYPERBOLIC SYSTEMS[J].Journal of Partial Differential Equations,2002,15(1):46-68. 被引量：4
2Wei Wei HAN1,2 1. Department of Applied Mathematics, Donghua University, Shanghai 201620, P. R. China,2. School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China.Asymptotic Behavior of Global Classical Solutions to the Cauchy Problem on a Semi-Bounded Initial Axis for Quasilinear Hyperbolic Systems[J].Journal of Mathematical Research and Exposition,2010,30(1):41-53. 被引量：1
3黄维章.对角型拟线性双曲系统在大初值下整体光滑解的存在性[J].应用数学学报,1991,14(2):229-233. 被引量：1
4韦真,杨永富.2×2线性退化系统初边值问题的显式解（英文）[J].复旦学报（自然科学版）,2017,56(1):34-39.
5罗李平,罗振国,曾云辉.一类带阻尼项的拟线性双曲系统的(全)振动性问题[J].山东大学学报（理学版）,2016,51(6):73-77.
6Quan ZHENG.Asymptotic Behavior of Global Classical Solutions to Quasilinear Hyperbolic Systems of Diagonal Form[J].Journal of Mathematical Research and Exposition,2010,30(1):29-40. 被引量：1
7李大潜,饶伯鹏.EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS[J].Acta Mathematica Scientia,2009,29(4):980-990. 被引量：1
8Yi ZHOU 11 Key Laboratory of Mathematics for Nonlinear Sciences,Ministry of Education,China,Shanghai Key Laboratory for Contemporary Applied Mathematics,School of Mathematical Sciences,Fudan University,Shanghai 200433,China..Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2011,32(5):771-780. 被引量：2
9WangLibin.FORMATION OF SINGULARITIES FOR QUASILINEAR HYPERBOLIC SYSTEMS WITH CHARACTERISTICS WITH CONSTANT MULTIPLICITY[J].Journal of Partial Differential Equations,2003,16(3):240-254. 被引量：1
10薛晓琳,刘存明.拟线性双曲型方程组Cauchy问题行波解的稳定性[J].数学学报（中文版）,2016,59(6):745-760.

Chinese Annals of Mathematics,Series B

2011年第6期

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