On the Cauchy problem for the wave equation with data on the boundary

We consider the Cauchy problem for the wave equation in $\Omega\times{\mathbb R}$withdatagivenonsomepartoftheboundary$\partial\Omega\times{\mathbb R}$. We provide a reconstruction algorithm for this problem based on analytic expressions. Our result is applicable to the problem of determining nonstationary wave field arising in geophysics, photoacoustic tomography, tsunami wave source recovery.