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GLOBAL SMOOTH SOLUTIONS FOR SEMILINEAR SCHRDINGER EQUATIONS WITH BOUNDARY FEEDBACK ON 2-DIMENSIONAL RIEMANNIAN MANIFOLDS 被引量：1

GLOBAL SMOOTH SOLUTIONS FOR SEMILINEAR SCHRDINGER EQUATIONS WITH BOUNDARY FEEDBACK ON 2-DIMENSIONAL RIEMANNIAN MANIFOLDS
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摘要 This paper considers the existence of global smooth solutions of semilinear schrSdinger equation with a boundary feedback on 2-dimensional Riemannian manifolds when initial data are small. The authors show that the existence of global solutions depends not only on the boundary feedback, but also on a Riemannian metric, given by the coefficient of the principle part and the original metric of the manifold. In particular, the authers prove that the energy of the system decays exponentially.
作者 Li DENG Pengfei YAO
机构地区 Key Laboratory of Control and Systems Graduate School of the Chinese Academy ofSciences Key Laboratory of Control and Systems
出处 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2009年第4期749-776,共28页 系统科学与复杂性学报（英文版）
基金 supported by the National Science Foundation of China under Grants Nos. 60225003, 60334040, 60221301, 60774025, and 10831007 Chinese Academy of Sciences under Grant No KJCX3-SYW-S01
关键词 Boundary feedback energy decay Riemannian metric semilinear schr6dinger equation. 全局光滑解 薛定谔方程 边界反馈 黎曼流形 半线性 人道主义 反应 黎曼度量
分类号 O413.1 [理学—理论物理] Q959.21 [生物学—动物学]
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参考文献13

  • 1P. F. Yao, Boundary controllability for the quasilinear wave equation, URL: http://arxiv.org/abs /math.AP/0603280.
  • 2R. Triggiani and X. Xu, Pointwise Carleman estimates, global uniqueness, observability, and stabilization for Schrodinger equations on Riemannian manifolds at the H^1(Ω)-level, AMS Contemporary Mathematics, 2007, 426: 339-404.
  • 3I. Lasiecka and R. Triggiani, Optimal regularity, exact controllability and uniform stabilization of the Schrodinger equation, Differential and Integral Equations, 1985, 5:521 -537.
  • 4E. Machtyngier and E. Zuazua. Stabilization of the schrodinger equation, Portugaliae Mathernatica, 1994, 51(2): 243-256.
  • 5S. E. Rebial, Uniform energy decay of Schrodinger equations with variable coefficients, IMA Journal of Mathematical Control and Information, 2003, 20:335-345.
  • 6R. Triggiani, Well-posedness and sharp uniform decay rates at the L^2(Ω)-level of the SchrSdinger equation with nonlinear boundary dissipation, J. Evol. Equ,. 2006, 6: 485--537.
  • 7C. Laurent, Global controllability and stabilization for the nonlinear Schrodinger equation on an interval, URL: http://arxiv.org/PScache/arxiv/pdf/0805/0805.3937v1.pdf.
  • 8S. Zhong, The growth in time of higher Sobolev norms of solutions to SchrSdinger equations on compact Riemannian manifolds, J. Differential Equations, 2008, 245: 359-376.
  • 9P. F. Yao, On the observability inequalities for exact controllability of wave equations with variable coefficients. SIAM J. Control Optim, 1999, 37(5): 1568-1599.
  • 10E. Machtyngier, Controlabilite exact et stabilisation frontiere de l'equation de Schrodinger, C.R. Acad. Sc. Paris, 1990, 310: 801-806.

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Journal of Systems Science & Complexity
2009年 第4期

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