论文标题
热方程的定量快速和有限的时间稳定
Quantitative rapid and finite time stabilization of the heat equation
论文作者
论文摘要
热方程式的无效可控性数十年[19,23,30]。 Coron-Nguyên[13]证明了一维热方程的有限时间稳定性，而高维空间的同样问题仍然广泛开放。受Coron-trélat[14]的启发，我们发现了明确的固定反馈定律，这些反馈定律在定量上以衰减速率$λ$和$ CE^{C \sqrtλ} $估计，在其中lebobeau-robbiano的光谱频谱的频谱[30]自然使用。然后，一个分段控制参数会导致零件可控性，最佳成本$ CE^{C/T} $以及有限的时间稳定。
The null controllability of the heat equation is known for decades [19,23,30]. The finite time stabilizability of the one dimensional heat equation was proved by Coron--Nguyên [13], while the same question for high dimensional spaces remained widely open. Inspired by Coron--Trélat [14] we find explicit stationary feedback laws that quantitatively exponentially stabilize the heat equation with decay rate $λ$ and $Ce^{C\sqrtλ}$ estimates, where Lebeau--Robbiano's spectral inequality [30] is naturally used. Then a piecewise controlling argument leads to null controllability with optimal cost $Ce^{C/T}$, as well as finite time stabilization.
