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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!

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Is is correct that $z=y$? –  András Bátkai May 4 '13 at 17:43
    
Are you supposing by any chance that $h(t)$ vanishes in a neighborhood of $t=0$ or $T$? –  Igor Khavkine May 4 '13 at 18:10
    
This is an interesting question but the $z$-$y$ ambiguity needs resolution to allow orogress. Waiting for the OP to speak up . . . –  drbobmeister May 4 '13 at 19:41
    
I meant "progress", not "orogress" ! –  drbobmeister May 4 '13 at 19:43
    
Looks like researcher edited his question. Cool! –  drbobmeister May 4 '13 at 20:35
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