论文标题
从圆环上的线段的分散方程可观察性
Observability of dispersive equations from line segments on the torus
论文作者
论文摘要
我们研究了圆环$ \ mathbb {t} $上一类线性分散方程的总类别的可观察性。我们将时空区域的一个线段或两个线段作为可观察的集合。我们赋予线段斜率的特征，以保证定性可观察性和定量可观察性。一行细分案例很简单，直接来自英格汉姆的不平等。但是，两个线段的情况很困难，结果的说明和证明很大程度上取决于图理论的语言。我们还将结果应用于（高阶）Schrödinger方程和线性KDV方程。
We investigate the observability of a general class of linear dispersive equations on the torus $\mathbb{T}$. We take one line segment or two line segments in space-time region as the observable set. We give the characteristic on the slopes of the line segments to guarantee the qualitative observability and quantitative observability respectively. The one line segment case, is simple, follows directly from the Ingham's inequality. However, the two line segments case is difficult, the statement of results and the proof rely heavily on the language of graph theory. We also apply our results to (higher order) Schrödinger equations and the linear KdV equation.
