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arXiv · 2409.06260

Lipschitz Stability of an Inverse Problem of Transmission Waves with Variable Jumps

L Baudouin·A Imba·A Mercado·A Osses
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Abstract

This article studies an inverse problem for a transmission wave equation, a system where the main coefficient has a variable jump across an internal interface given by the boundary between two subdomains. The main result obtains Lipschitz stability in recovering a zeroth-order coefficient in the equation. The proof is based on the Bukhgeim-Klibanov method and uses a new one-parameter global Carleman inequality, specifically constructed for the case of a variable main coefficient which is discontinuous across a strictly convex interface. In particular, our hypothesis allows the main coefficient to vary smoothly within each subdomain up to the interface, thereby extending the preceding literature on the subject.

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L Baudouin, A Imba, A Mercado, A Osses. 2024-09-10. Lipschitz Stability of an Inverse Problem of Transmission Waves with Variable Jumps. https://arxiv.org/abs/2409.06260

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