论文标题
低纤维化Ornstein-uhlenbeck方程的近似零可控性和均匀成本
Approximate null-controllability with uniform cost for the hypoelliptic Ornstein-Uhlenbeck equations
论文作者
论文摘要
我们证明，在$ \ mathbb r^n $上构成的低纤维化Ornstein-uhlenbeck方程均匀成本的近似零可控性的特征是控制支架上的整体厚度几何条件。我们还提供相关的定量弱可观察性估计值。对于一类大量非自主椭圆方程，从同一研究中得出了低纤维化的Ornstein-Uhlenbeck方程的结果。我们特别概括了以$ \ Mathbb r^n $构成的抛物线方程而闻名的结果，通过厚度的概念，可以确保其近似无效的可控制性，而厚度的概念比当前工作中考虑的整体厚度条件更强。这些抛物线方程的示例是与操作员$（-δ）^s $相关的分数热方程，在制度$ s \ geq1/2 $中。我们的策略还允许表征该类别的分数热方程的移动控制支撑，以均匀的成本来表征近似的无效控制性。
We prove that the approximate null-controllability with uniform cost of the hypoelliptic Ornstein-Uhlenbeck equations posed on $\mathbb R^n$ is characterized by an integral thickness geometric condition on the control supports. We also provide associated quantitative weak observability estimates. This result for the hypoelliptic Ornstein-Uhlenbeck equations is deduced from the same study for a large class of non-autonomous elliptic equations from moving control supports. We generalize in particular results known for parabolic equations posed on $\mathbb R^n$, for which the approximate null-controllability with uniform cost is ensured by the notion of thickness, which is stronger that the integral thickness condition considered in the present work. Examples of those parabolic equations are the fractional heat equations associated with the operator $(-Δ)^s$, in the regime $s\geq1/2$. Our strategy also allows to characterize the approximate null-controllability with uniform cost from moving control supports for this class of fractional heat equations.
