论文标题
有限的时间稳定和动态边界条件的热方程式的冲动控制
Finite-time stabilization and impulse control of heat equation with dynamic boundary conditions
论文作者
论文摘要
在本文中，我们研究了具有动态边界条件的多维热方程的冲动可控性。使用基于有限时间稳定的最新方法，我们表明该系统在任何积极的时间都可以通过在物理域的非空式开放子集中支持的任何积极时间脉冲控制。此外，我们推断出解决方案指数衰减的明确估计值。主要结果的证明结合了对数凸度估计值和与动态边界条件相关的一些光谱特性。在我们的环境中，夫妇实体现象的方程式的性质使得有必要进行相当复杂的估计，并结合几个边界项。
In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is impulse null controllable at any positive time via impulse controls supported in a nonempty open subset of the physical domain. Furthermore, we infer an explicit estimate for the exponential decay of the solution. The proof of the main result combines a logarithmic convexity estimate and some spectral properties associated to dynamic boundary conditions. In our setting, the nature of the equations, which couple intern-boundary phenomena, makes it necessary to go into quite sophisticated estimates incorporating several boundary terms.
