发表机构
Aix-Marseille université（艾克斯-马赛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究两类线性抛物型系统的边界近似可控性，提出充分条件并证明一维单控制下的必要性，给出矩形域刻画，并构造分布可控但边界不可控的级联系统。
AI 中文摘要
本文研究两类线性抛物型系统的边界近似可控性，即通过常数项耦合的$n$个热方程系统，以及通过具有空间依赖系数的一阶偏微分算子耦合的$2 \ imes 2$级联系统。对于每个系统，我们在任意空间维度下证明了一个充分条件，并表明在仅有一个控制的一维情形下，该条件也是必要的。对于耦合热方程系统，我们还研究了矩形域上的问题，并根据控制域的位置给出了刻画。最后，我们构造了一个级联系统，其分布可控性成立而边界可控性不成立。该方法依赖于H.O. Fattorini的一个一般性刻画。
英文摘要
This paper focuses on the boundary approximate controllability of two classes of linear parabolic systems, namely a system of $n$ heat equations coupled through constant terms and a $2 \times 2$ cascade system coupled by means of a first order partial differential operator with space-dependent coefficients. For each system we prove a sufficient condition in any space dimension and we show that this condition turns out to be also necessary in one dimension with only one control. For the system of coupled heat equations we also study the problem on rectangle, and we give characterizations depending on the position of the control domain. Finally, we exhibit a cascade system for which the distributed controllability holds whereas the boundary controllability does not. The method relies on a general characterization due to H.O. Fattorini.
Journal refEvol. Equ. Control Theory 3 (2014), no. 1, 167-189
