论文标题
关于临界长度的KDV系统的小型局部可控性
On the small-time local controllability of a KdV system for critical lengths
论文作者
论文摘要
本文专用于非线性KDV方程的局部无效控制性，使用右侧的Neumann边界控制配备了Dirichlet边界条件。 Rosier证明，该KDV系统对于所有非关键长度都是局部可控的，而线性化系统的不可控制的空间是有限的，当长度至关重要时。关于临界长度，Coron和Crépeau表明，当线性化系统的不可控制空间为尺寸1，然后Cerpa，然后Cerpa和Crépeau确定局部可控性在所有其他关键长度的有限时间内保持时。在本文中，我们证明，对于一类关键长度，非线性KDV系统是{\ it not}的小型本地可控。
This paper is devoted to the local null-controllability of the nonlinear KdV equation equipped the Dirichlet boundary conditions using the Neumann boundary control on the right. Rosier proved that this KdV system is small-time locally controllable for all non-critical lengths and that the uncontrollable space of the linearized system is of finite dimension when the length is critical. Concerning critical lengths, Coron and Crépeau showed that the same result holds when the uncontrollable space of the linearized system is of dimension 1, and later Cerpa, and then Cerpa and Crépeau established that the local controllability holds at a finite time for all other critical lengths. In this paper, we prove that, for a class of critical lengths, the nonlinear KdV system is {\it not} small-time locally controllable.
