论文标题
关于具有不可用的扩散矩阵的抛物线系统的可控性的评论
Remarks on the controllability of parabolic systems with non-diagonalizable diffusion matrix
论文作者
论文摘要
在恒定矩阵的情况下，已经研究了具有降低的对照数量的耦合抛物线系统的分布式无效系统的分布式无可控性。另一方面，尚不完全了解具有这种系统的非恒定系数的边界可控性问题和分布式可控性。在本文中，我们分析了一类耦合的抛物线系统的边界可控性能在恒定情况下具有不可用的扩散矩阵，以及具有空间依赖性系数的2 x 2不可降落伞系统的分布式可控性。对于边界可控性问题，我们的策略依赖于当下方法。对于分布式可控性问题，我们的发现通过使用Fattorini-Hautus测试和虚拟控制策略提供了积极和负面的控制结果。
The distributed null controllability for coupled parabolic systems with non-diagonalizable diffusion matrices with a reduced number of controls has been studied in the case of constant matrices. On the other hand, boundary controllability issues and distributed controllability with non-constant coefficients for this kind of systems is not completely understood. In this paper, we analyze the boundary controllability properties of a class of coupled parabolic systems with non-diagonalizable diffusion matrices in the constant case and the distributed controllability of a 2 x 2 non-diagonalizable parabolic system with space-dependent coefficients. For the boundary controllability problem, our strategy relies on the moment method. For the distributed controllability problem, our findings provide positive and negative control results by using the Fattorini-Hautus test and a fictitious control strategy.
