SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 539-562, February 2024.
Abstract. The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE’s posed on the two-dimensional torus [math]. The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin–Ono and Korteweg–de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in the Sobolev space [math], with [math], by constructing an appropriated feedback control law.

中文翻译：

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二维环面上线性色散偏微分方程的精确可控性和稳定性

SIAM 控制与优化杂志，第 62 卷，第 1 期，第 539-562 页，2024 年 2 月。
摘要。矩方法用于证明在二维环面上提出的一类广泛的二维线性色散偏微分方程的精确可控性[数学]。控制函数被认为作用于环面的一个小的垂直和水平条带上。我们的结果适用于几个著名的模型，包括 Benajamin-Ono 和 Korteweg-de Vries 方程的一些二维扩展。作为副产品，通过构建适当的反馈控制律，在 Sobolev 空间 [数学] 中也建立了任何给定衰减率的指数稳定性。