This paper is concerned with the null controllability of a cascade
linear system formed by a heat and a wave equation in a cylinder $\Omega \times
The control acts only on the heat equation and is supported by a set
of the form $\omega \times (0,T)$, where $\omega \subset \Omega$.
In the wave equation, only the restriction of the solution to the heat
equation to another set $\mathcal O \times (0,T)$ appears.
In the main result in this paper, we show that, under appropriate
assumptions on $T$, $\omega$ and $\mathcal O$, the system is null controllable.
Mathematics Subject Classification: 93B05, 93B07, 93C20, 35M20.