Year: 2025
Type: article
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.
Source: Inverse Problems
Authors: L Baudouin, A Imba, A Mercado, A Osses
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: Centro de Modelamiento Matemático, Facultad de Ciencias Físicas y Matemáticas, Agencia Nacional de Investigación y Desarrollo, Fondo Nacional de Desarrollo Científico y Tecnológico, Fondo de Fomento al Desarrollo Científico y Tecnológico, Fondo de Financiamiento de Centros de Investigación en Áreas Prioritarias
Awards: CENTRO DE CIENCIA DEL CLIMA Y LA RESILENCIA (CR)2, G146908162, G2072514181, G2478467581, G2522673491, G2549737163, CARLEMAN ESTIMATES FOR SOME PARTIAL DIFFERENTIAL EQUATIONS WITH NON-HOMOGENEOUS BOUNDARY CONDITIONS AND APPLICATIONS TO CONTROLLABILITY, G3612929074, G4481024449, G465644580, SCIENCE-POLICY INTERFACES AND SCENARIO CONSTRUCTION IN CHILE HOW TO BETTER BRIDGE SCIENTIFIC EVIDENCE WITH POLICY-MAKING? AN INTER-TRANSDISCIPLINARY CHALLENGE FOR ENVIRONMENTAL COMPLEX PROBLEMS., G5079548756, G5367379007, G5695274896, G621937651, G7177034782, G7236899919, INVERSE PROBLEMS FOR WAVES AND PHOTON PROPAGATION ARISING IN MEDICAL IMAGING AND MICROSCOPY, CENTER FOR MATHEMATICAL MODELING (CMM)
OpenAlex ID: W4408433971