Lipschitz Stability of an Inverse Problem of Transmission Waves with Variable Jumps - Équipe Méthodes et Algorithmes en Commande
Pré-Publication, Document De Travail Année : 2024

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

Résumé

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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Dates et versions

hal-04688851 , version 1 (06-09-2024)

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Lucie Baudouin, A Imba, A Mercado, A Osses. Lipschitz Stability of an Inverse Problem of Transmission Waves with Variable Jumps. 2024. ⟨hal-04688851⟩
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