论文标题
传播速度未知速度的波方程的平均可控性的数值近似
Numerical approximation of the averaged controllability for the wave equation with unknown velocity of propagation
论文作者
论文摘要
我们提出了一种数值方法，以根据未知参数sigma近似波浪方程的精确平均边界控制。更确切地说，与Sigma无关的控制将初始数据驱动到时间t = t的最终状态家族，其平均是Sigma的平均值。这个想法是在Laplace操作员的第一个本征函数生成的有限维空间中投射控制问题。每当连续的控制问题中，最终的离散控制问题就有解决方案，我们给出了离散控制的收敛结果。该方法在正方形域中的1-D和2-D中的几个示例进行了说明。
We propose a numerical method to approximate the exact averaged boundary control of a family of wave equations depending on an unknown parameter sigma. More precisely the control, independent of sigma, that drives an initial data to a family of final states at time t = T, whose average in sigma is given. The idea is to project the control problem in the finite dimensional space generated by the first N eigenfunctions of the Laplace operator. The resulting discrete control problem has solution whenever the continuous one has it, and we give a convergence result of the discrete controls to the continuous one. The method is illustrated with several examples in 1-d and 2-d in a square domain.
