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- #1

$\begin{aligned} & {{u}_{tt}}=9{{u}_{xx}},\text{ }x\in \mathbb{R},\text{ }t>0, \\

& u(x,0)=\left\{ \begin{align}

& 1,\text{ }x\in [1,2] \\

& 0,\text{ }x\notin [1,2] \\

\end{align} \right. \\

& {{u}_{t}}(x,0)=0,

\end{aligned}

$

then determine the points of the semiplane $t>0$ where $u(x,t)=0.$

Okay I know the D'Lembert's formula, but I don't know how to apply it since having $u(x,0)$ defined by two conditions.

Thanks!