[1] HAO C,LING H,WANG B.Well-posedness for the fourth order nonlinear Schrödinger equations [J].Journal of Mathematical Analysis and Applications,2006,320(1):246-265. [2] HAO C,LING H,WANG B.Well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in multi-dimensional spaces [J].J Math Anal Appl,2007,328:58-83. [3] PAUSADER B.Global well-posedness for energy-critical fourth-order Schrödinger equations in the radial case [J].Dynamics of Partial Differential Equations,2007,4(3):197-225. [4] PAUSADER B.The cubic fourth-order Schrödinger equation [J].Journal of FunctionalAnalysis,2009,256(8):2473-2517. [5] REN Y Y,LI Y S,YAN W.Sharp well-posedness of the Cauchy problem for the fourthorder nonlinear Schrödinger equation [J].Communications on Pure and Applied Analysis,2018,17(2):487-504. [6] LASIECKA I,TRIGGIANI R.Optimal regularity,exact controllability and uniform stabilization of Schrödinger equations with Dirichlet control [J].Differential Integral Equations,1992,5(3):521-535. [7] GUO B Z,SHAO Z C.Well-posedness and regularity for non-uniform Schrödingerand Euler-Bernoulli equations with boundary control and observation [J].Quarterly of Applied Mathematics,2012,70:111-132. [8] MILLER L.Controllability cost of conservative systems: resolvent condition and transmutation [J].Journal of Functional Analysis,2005,218(2):425-444. [9] WEN R L,CHAI S G,GUO B Z.Well-posedness and exact controllability of fourth-order Schrödinger equation with hinged boundary control and collocated observation [J].Mathematics of Control Signals & Systems,2016,28(3):1-28. [10] GUO B Z,ZHANG X.The regularity of the wave equation with partial Dirichlet control and collocated observation [J].SIAM J Control Optim,2005,44(5):1598-1613. [11] TUCSNAK M,WEISS G.Observation and control for operator semigroups [M].Basel:Birkhäuser Verlag,2009. [12] LIONS J L,MAGENES E.Non-Homogeneous boundary value problems and applications,Vol.I [M].Berlin:Springer-Verlag,1972. [13] PAZY A.Semigroups of linear operators and applications to partial differential equations [M].New York:Springer-Verlag,1983. [14] 郭宝珠,柴树根.无穷维线性系统控制理论 [M].北京:科学出版社,2012. [15] YAO P F,FENG D X.Structure for nonnegative square roots of unbounded nonnegative selfadjoint operators [J].Quart Appl Math,1996,54(3):457-473. [16] GUO B Z,SHAO Z C.Regularity of an Euler-Bernoulli equation with Neumann control and collocated observation [J].J Dyn Control Syst,2006,12(3):405-418. [17] WEISS G.Transfer functions of regular linear systems.I.Characterizations of regularity [J].Trans Amer Math Soc,1994,342(2):827-854. [18] KOMORNIK V.Exact controllability and stabilization:The multiplier method [M].Paris:John Wiley Chichester,1994. [19] CAZENAVE T.An introduction to nonlinear Schrödinger equations [M].Rio de Janeiro:Textos de Métodos Matemáticos,1996. [20] SIMON J.Compact sets in the space Lp(0,T;B) [J].Annali di Matematica Pura ed Applicata,1987,146(1):65-96. [21] HÖRMANDER L.Linear partial differential operators [M].Berlin:Springer-Verlag,1976. |