论文标题
Carleman估计超出纤维操作员的估算值和波动方程的内部控制
Carleman Estimate for Ultrahyperbolic Operators and Improved Interior Control for Wave Equations
论文作者
论文摘要
在本文中，我们介绍了一个针对Ultrahyperbolic操作员的小说Carleman估计，以$ \ mathbb {r}^m_t \ times \ times \ mathbb {r}^n_x $。然后，我们使用此估计值的特殊情况来获得具有时间依赖性下阶项的波方程的改进可观察性结果。关键的改进是：（1）与标准Carleman估计结果相比，我们获得了较小的观察区域，并且（2）当观测点位于域内时，我们也证明了可观察到的效率。最后，作为可观察性结果的推论，我们获得了波动方程的内部可控性。
In this article, we present a novel Carleman estimate for ultrahyperbolic operators, in $ \mathbb{R}^m_t \times \mathbb{R}^n_x $. Then, we use a special case of this estimate to obtain improved observability results for wave equations with time-dependent lower order terms. The key improvements are: (1) we obtain smaller observation regions compared to standard Carleman estimate results, and (2) we also prove observability when the observation point lies inside the domain. Finally, as a corollary of the observability result, we obtain improved interior controllability for the wave equation.
