论文标题
$ l^1 $和$ l^2 $空间中波方程的两点边界价值问题的可控性：一个维情况
Controllability of two-point boundary value problem for wave equations in $L^1$ and $L^2$ spaces: One dimensional case
论文作者
论文摘要
在本文中，我们讨论了一维波方程的两点边界值问题（TBVP）的可控性。引入了一些新概念：TBVP输入控制问题，最小输入解决方案（MS）和最低输入溶液（PMS）。我们将公制设置为$ l^1 $，$ l^2 $空间在封闭的集合中设置，并控制输入以达到最低。我们主要讨论输入的属性，分别以$ l^1 $和$ l^2 $公制的MS和PMS的存在和独特性。最低输入位于$ l^1 $的条带上，$ l^1 $，$ l^2 $始终存在。此外，为了构建PM，我们还引入了一种符合某些条件的近似方法。
In this paper we discuss the controllability of two-point boundary value problem (TBVP) for one-dimensional wave equation. Some new concepts are introduced: TBVP input control problem, minimum-input solution (MS) and pre-minimum-input solution (PMS). We set the metric in $L^1$ and $L^2$ spaces on a closed set, and control the input to reach its minimum. And we mainly discuss the property of input, the existence and uniqueness of MS and PMS for $L^1$ and $L^2$ metric respectively. The minimum inputs lie on a strip in $L^1$ and PMS for $L^1$ and $L^2$ always exists. Furthermore, to construct PMS, we also introduce an approximation method which meets certain conditions.
