Abstract
The boundary controllability of the fourth order Schrödinger 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(Ω) for an arbitrarily small time. The method of proof combines both the HUM (Hilbert Uniqueness Method) and multiplier techniques.
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Project supported by 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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Zheng, C., Zhou, Z. Exact controllability for the fourth order Schrödinger equation. Chin. Ann. Math. Ser. B 33, 395–404 (2012). https://doi.org/10.1007/s11401-012-0711-6
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DOI: https://doi.org/10.1007/s11401-012-0711-6