论文标题
线性色散PDE在二维圆环上的确切可控性和稳定性
Exact controllability and stabilization for linear dispersive PDE's on the two-dimensional torus
论文作者
论文摘要
力矩方法用于证明在二维圆环$ \ mathbb {t}^{2}上构成的一类宽类线性色散PDE的确切可控性。我们的结果适用于几个知名模型，包括Benajamin-Ono和Korteweg-de Vries方程的一些二次扩展。作为一个产品，还以任何给定的衰减率的指数稳定性在$ h^{s} _ {p}中建立（\ Mathbb {t}^{2}），$ s \ geq 0，$，通过构建分配的反馈控制法。
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 $\mathbb{T}^{2}.$ 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 $H^{s}_{p}(\mathbb{T}^{2}),$ with $s\geq 0,$ by constructing an appropriated feedback control law.
