Is it possible find a computable solution to the following homogeneous wave equation problem: Let $\mathcal{C}=\{(x,y,z)\in \mathbb{R}^3, 0< x,y,z < 1\} $ be the open unit cube. Find $u$ such that \begin{align*} &\partial_t^2 -\Delta u =0, ~(t,\hat{x})\in \mathbb{R}^+\times \mathcal{C} \\ &u(0,x)=\partial_tu(0,x)=0 ,~\hat{x} \in \overline{\mathcal{C}} \end{align*}
Any help would be greatly appreciated.