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| Exact Controllability for the Fourth Order Schr¨odinger Equation |
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Citation： |
Chuang ZHENG,Zhongcheng ZHOU.Exact Controllability for the Fourth Order Schr¨odinger Equation[J].Chinese Annals of Mathematics B,2012,33(3):395~404 |
| Page view： 1999
Net amount： 1402 |
Authors： |
Chuang ZHENG; Zhongcheng ZHOU; |
Foundation： |
the Fundamental Research Funds for the Central Universities (No.\ XDJK2009C099), the National Natural Science Foundation of China (Nos.\ 11001018, 11026111) and the Specialized Research Fund for the Doctoral Program of Higher Education (No.\ 201000032006). |
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| Abstract： |
The boundary controllability of the fourth order Schr¨odinger equation in a bounded domain is studied. By means of an $L^2$-Neumann boundary control, the authors prove that the solution is exactly controllable in $H^{-2}(\Omega)$ for an arbitrarily small time. The method of proof combines both the HUM (Hilbert Uniqueness Method) and multiplier techniques. |
Keywords： |
Fourth order Schr¨odinger equation, HUM method, Controllability,Multiplier |
Classification： |
93B05, 35Q40, 93C20 |
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