期刊文献+

Exact Controllability for the Fourth Order Schrdinger Equation 被引量:1

Exact Controllability for the Fourth Order Schrdinger Equation
原文传递
导出
摘要 The boundary controllability of the fourth order Schr5dinger equation in a bounded domain is studied. By means of an L2-Neumann boundary control, the authors prove that the solution is exactly controllable in H-2(12) for an arbitrarily small time. The method of proof combines both the HUM (Hilbert Uniqueness Method) and multiplier techniques.
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2012年第3期395-404,共10页 数学年刊(B辑英文版)
基金 supported by the Fundamental Research Funds for the Central Universities (No. XDJK2009C099) the National Natural Science Foundation of China (Nos. 11001018,11026111) the Specialized Research Fund for the Doctoral Program of Higher Education (No. 201000032006)
关键词 Fourth order Schroedinger equation HUM method CONTROLLABILITY MULTIPLIER 方程 四阶 边界能控性 边界控制 倍频技术 希尔伯特 时间
  • 相关文献

参考文献20

  • 1Bardos, C., Lebeau, G. and Rauch, J., Sharp sufficient conditions for the observation, control and stabi- lization of waves from the boundary, SIAM J. Control Optim., 30, 1992, 1024-1065.
  • 2Burq, N. and Zworski, M., Geometric control in the presence of a black box, J. Amer. Math. Soc., 17, 2004, 443-471.
  • 3Chou, H. and Guo, Y., Null boundary controllability for a fourth order semilinear equation, Taiwan Residents J. Math., 10, 2006, 251-263..
  • 4Diaz, J. I. and Ramos, A. M., On the approximate controllability for higher order parabolic nonlinear equations of Cahn-Hilliard type, Internat. Set. Numer. Math., 126, 1998, 111-127.
  • 5Fu, X., Yong, J. and Zhang, X., Controllability and observability of a heat equation with hyperbolic memory kernel, J. Differential Equations, 247, 2009, 2395-2439.
  • 6Fursikov, A. and Imanuvilov, O., Controllability of Evolution Equations, Lecture Notes Series, Vol. 34, Seoul National University, Seoul, 1996.
  • 7Hao, C., Hsiao, L. and Wang, B., Wellposedness for the fourth order nonlinear Schr6dinger equations, J. Math. Anal. Appl., 320, 2006, 246 265.
  • 8Hao, C., Hsiao, L. and Wang, B., Well-posedness of Cauchy problem for the fourth order nonlinear SchrSdinger equations in multi-dimensional spaces, J. Math. Anal. Appl., 328, 2007, 58-83.
  • 9Hormander, L., Linear Partial Differential Operators, Springer-Verlag, Berlin, 1976.
  • 10Lin, P. and Zhou, Z., Observability estimate for a one-dimensional fourth order parabolic equation, Pro- ceedings of the 29th Chinese Control Conference, China, 2010, 830-832.

引证文献1

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部