  In the paper, the problems of controllability and approximate controllability
are studied for the control system
$w_t=\frac{1}{\rho}\left(kw_x\right)_x+\gamma w$,
$\left.\left(\sqrt{\frac{k}{\rho}}w_x\right)\right|_{x=0}=u$, $x>0$,
$t\in(0,T)$, 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 $\rho$, $k$, $\gamma$ is applied. The
results are illustrated by examples.
