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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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    $\begingroup$ Is is correct that $z=y$? $\endgroup$
    – András Bátkai
    Commented May 4, 2013 at 17:43
  • $\begingroup$ Are you supposing by any chance that $h(t)$ vanishes in a neighborhood of $t=0$ or $T$? $\endgroup$
    – Igor Khavkine
    Commented May 4, 2013 at 18:10
  • $\begingroup$ This is an interesting question but the $z$-$y$ ambiguity needs resolution to allow orogress. Waiting for the OP to speak up . . . $\endgroup$
    – drbobmeister
    Commented May 4, 2013 at 19:41
  • $\begingroup$ I meant "progress", not "orogress" ! $\endgroup$
    – drbobmeister
    Commented May 4, 2013 at 19:43
  • $\begingroup$ Looks like researcher edited his question. Cool! $\endgroup$
    – drbobmeister
    Commented May 4, 2013 at 20:35

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