论文标题
具有动态边界条件的1-D热方程的对数凸度和冲动可控性
Logarithmic convexity and impulsive controllability for the 1-D heat equation with dynamic boundary conditions
论文作者
论文摘要
在本文中，我们证明了一个对数凸度，它反映了具有动态边界条件的1-D热方程的单个时间点的可观察性估计值。因此，我们建立了具有动态边界条件的冲动热方程的冲动近似可控性。此外，我们获得了冲动控制成本的明确上限。最后，我们给出了一种建设性算法，用于计算最小$ l^2 $ -Norm的冲动控制。我们还提出了一些数值测试来验证理论结果并显示了设计算法的效率。
In this paper, we prove a logarithmic convexity that reflects an observability estimate at a single point of time for 1-D heat equation with dynamic boundary conditions. Consequently, we establish the impulse approximate controllability for the impulsive heat equation with dynamic boundary conditions. Moreover, we obtain an explicit upper bound of the cost of impulse control. At the end, we give a constructive algorithm for computing the impulsive control of minimal $L^2$-norm. We also present some numerical tests to validate the theoretical results and show the efficiency of the designed algorithm.
