Recover all Coefficients in Second-Order Hyperbolic Equations from Finite Sets of Boundary Measurements

2022/10/08 by Shitao Liu, Liu, Shitao, Antonio Pierrottet +3
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.2210.03865

openalex publication_date 2022/10/08 · openalex created_date 2022/10/12 · openalex updated_date 2026/07/28

Abstract

We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on an open bounded domain with smooth enough boundary. We show that by appropriately selecting finite pairs of initial conditions we can uniquely and Lipschitz stably recover all those coefficients from the corresponding boundary measurements of their solutions. The proofs are based on sharp Carleman estimate, continuous observability inequality and regularity theory for general second-order hyperbolic equations.

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