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

2018/10/30 by M. N. Demchenko, Demchenko, M. N.
Earth and Planetary Sciences · Engineering · Mathematics · #35L05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Seismic Imaging and Inversion Techniques #math.AP #msc:35L05

paper · pdf · doi:10.48550/arxiv.1810.12631

arxiv created 2018/10/30 · openalex publication_date 2018/10/30 · arxiv updated 2018/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem for the wave equation in Ω×\mathbb R with data given on some part of the boundary ∂Ω×\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.

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