论文标题
结构抑制板动力学的无效控制器的数值近似
Numerical Approximations for the Null Controllers of Structurally Damped Plate Dynamics
论文作者
论文摘要
在本文中，我们考虑了在铰链边界条件下结构阻尼的弹性方程。为这些抛物线样PDE的零可控性生成了全差异数值近似方案。我们主要使用有限元方法（FEM）和有限差法（FDM）近似值，以表明通过FEM和FDM近似的零控制器表现出相关最小能量函数的渐近学。为此，我们呼吁R. Triggiani [20]最初给出的理论用于构建ODE Systems的无效控制器。这些无效控制器也适合我们的数值实现，其中我们讨论了FEM和FDM数值近似的方面，并比较这两种方法。我们通过对两个近似方案给出的数值实验证明了我们的理论结果。
In this paper, we consider a structurally damped elastic equation under hinged boundary conditions. Fully-discrete numerical approximation schemes are generated for the null controllability of these parabolic-like PDEs. We mainly use finite element method (FEM) and finite difference method (FDM) approximations to show that the null controllers being approximated via FEM and FDM exhibit exactly the same asymptotics of the associated minimal energy function. For this, we appeal to the theory originally given by R. Triggiani [20] for construction of null controllers of ODE systems. These null controllers are also amenable to our numerical implementation in which we discuss the aspects of FEM and FDM numerical approximations and compare both methodologies. We justify our theoretical results with the numerical experiments given for both approximation schemes.
