论文标题
具有稀疏传感器的二次抛物线微分方程的控制问题，有限的音量或各向异性衰减密度
Control problem for quadratic parabolic differential equations with sparse sensor sets of finite volume or anisotropically decaying density
论文作者
论文摘要
我们证明了二次抛物线微分方程的可观察性和无效控制性。如果发电机具有微不足道的奇异空间$ S $，则允许传感器组稀疏并具有有限的体积。对于具有单数空间的发电机$ s \ neq \ {0 \} $，传感器集可以在由$ s $确定的方向上衰减。该证明是基于二次差异操作员在部分谐波振荡器和相应不确定性关系的光谱投影方面的耗散估计。
We prove observability and null-controllability for quadratic parabolic differential equations. The sensor set is allowed to be sparse and have finite volume if the generator has trivial singular space $S$. In the case of generators with singular space $S \neq \{0\}$ the sensor set is permitted to decay in directions determined by $S$. The proof is based on dissipation estimates for the quadratic differential operator with respect to spectral projections of partial harmonic oscillators and corresponding uncertainty relations.
