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Asymptotic behavior of a Schrödinger equation under a constrained boundary feedback

  • * Corresponding author: Dongyi Liu

    * Corresponding author: Dongyi Liu 
This research is supported by the Natural Science Foundation of China grant NSFC-61573252.
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  • Design of controller subject to a constraint for a Schrödinger equation is considered based on the energy functional of the system. Thus, the resulting closed-loop system is nonlinear and its well-posedness is proven by the nonlinear monotone operator theory and a complex form of the nonlinear Lax-Milgram theorem. The asymptotic stability and exponential stability of the system are discussed with the LaSalle invariance principle and Riesz basis method, respectively. In the end, a numerical simulation illustrates the feasibility of the suggested feedback control law.

    Mathematics Subject Classification: Primary: 93D15, 93D20; Secondary: 35B40.


    \begin{equation} \\ \end{equation}
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  • Figure 1.  Real part of $w(x, t)$

    Figure 2.  Imaginary part of $w(x, t)$

    Figure 3.  Real and imaginary parts of $w(1, t)$

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