论文标题
热方程式的可控性问题，其在由Neumann边界条件控制的半轴上可变系数
Controllability Problems for the Heat Equation with Variable Coefficients on a Half-Axis Controlled by the Neumann Boundary Condition
论文作者
论文摘要
在本文中，研究系统的可控性和近似可控性问题$ w_t = \ frac {1}ρ\ left（kw_x \ first）_x+γw$，$ \ left。\ left。 $ t \ in（0，t）$，其中$ u $是控制，$ u \ in l^\ infty（0，t）$。证明控制系统的每个初始状态在给定时间$ t> 0 $中近似可控与任何目标状态。为了获得此结果，应用了方程数据$ρ$，$ k $，$γ$生成的转换操作员。结果通过示例说明。
In the paper, the problems of controllability and approximate controllability are studied for the control system $w_t=\frac{1}ρ\left(kw_x\right)_x+γw$, $\left.\left(\sqrt{\frac{k}ρ}w_x\right)\right|_{x=0}=u$, $x>0$, $t\in(0,T)$, where $u$ is a control, $u\in L^\infty(0,T)$. It is proved that each initial state of the control system is approximately controllable to any target state in a given time $T>0$. To obtain this result, the transformation operator generated by the equation data $ρ$, $k$, $γ$ is applied. The results are illustrated by examples.
