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 $(z,z_t)$ vanish at $T$, i.e $z(T)=z_t(T)=0$.

Thanks!