Consider the linear wave equation :

$$z_{tt}=\Delta z + k(x) z + h(t) , \; in \; \Omega\times (0,T)$$

Are there sufficient conditions on the functions $k(x)$ and $h(t)$ for which $(y,y_t)$ vanish at $T$, i.e $y(T)=y_t(T)=0$.

Thanks!