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

TL;DR

This paper presents an analytic reconstruction algorithm for the wave equation's Cauchy problem with boundary data, applicable to geophysics, photoacoustic tomography, and tsunami source recovery.

Contribution

It introduces a novel analytic method for solving the wave equation Cauchy problem with boundary data, enhancing applications in geophysics and medical imaging.

Findings

Reconstruction algorithm based on analytic expressions

Applicable to geophysics and photoacoustic tomography

Improves wave source recovery techniques

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.