一类具有动力边界条件的薛定谔方程的精确能控性
Exact Controllability for a Schrödinger equation with dynamic boundary conditions
摘要：
本文研究了具有混合边界条件的薛定谔方程在边界的不相交子集上的能控性：Wentzell型动态边界条件和Dirichlet边界条件.本文的主要结果是通过相关伴随系统的新Carleman估计给出的，其中构造了专门适应域几何形状的权函数。利用这些估计，我们证明了系统的精确可控性与边界控制只作用在边界的Dirichlet条件的一部分。此外，我们还得到了系统的分布精确能控性结果。
英文摘要：
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.
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