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

Abstract

We consider the Cauchy problem for the wave equation in $\Omega \times \mathbb{R}$ with data given on some part of the boundary $\partial \Omega \times \mathbb{R}$. 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.