SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3501-3525, December 2023.
Abstract. In this paper, we study the controllability of a Schrödinger equation with mixed boundary conditions on disjoint subsets of the boundary: dynamic boundary condition of Wentzell type and Dirichlet boundary condition. The main result of this article is given by new Carleman estimates for the associated adjoint system, where the weight function is constructed specially adapted to the geometry of the domain. Using these estimates, we prove the exact controllability of the system with a boundary control acting only in the part of the boundary where the Dirichlet condition is imposed. Also, we obtain a distributed exact controllability result for the system.

中文翻译：

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具有动态边界条件的薛定谔方程的精确可控性

SIAM 控制与优化杂志，第 61 卷，第 6 期，第 3501-3525 页，2023 年 12 月。
摘要。在本文中，我们研究了具有混合边界条件的薛定谔方程在边界不相交子集上的可控性：Wentzell 型动态边界条件和 Dirichlet 边界条件。本文的主要结果是由相关伴随系统的新卡尔曼估计给出的，其中权重函数是专门根据域的几何结构构建的。使用这些估计，我们证明了系统的精确可控性，边界控制仅作用于施加狄利克雷条件的边界部分。此外，我们还获得了系统的分布式精确可控性结果。