@article{Fardigola_2018, title={Transformation operators in controllability problems for the degenerate wave equation with variable coefficients}, volume={70}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/1623}, abstractNote={We study the control system $w_{tt} = \cfrac1{\rho }
(kw_x) x + \gamma w,\; w(0, t) = u(t),\; x \in (0, l), t \in (0, T)$, in special modified spaces
of the Sobolev type. Here, $\rho , k,$ and \gamma are given functions on $[0, l)$; $u \in L^{\infty} (0, T)$ is a control, and $T > 0$ is a constant.
The functions $\rho$ and $k$ are positive on $[0, l)$ and may tend to zero or to infinity as $x \rightarrow l$. The growth of distributions from these spaces is determined by the growth of $\rho$ and $k$ as $x \rightarrow l$. Applying the method of transformation operators,
we establish necessary and sufficient conditions for the $L^{\infty}$ -controllability and approximate $L^{\infty}$ -controllability at a given
time and at a free time.
}, number={8}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Fardigola, L. V.}, year={2018}, month={Aug.}, pages={1128-1142} }