Stability and uniqueness for inverse problems for parabolic equations with final overdetermination*
O. Y. Imanuvilov, M. Yamamoto
article (Uluslararası, Hakemli) | Yazar(lar): O. Y. Imanuvilov, M. Yamamoto | Yıl: 2026 | Dergi/Kurum: INVERSE PROBLEMS | İndeks: WOS.SCI | DOI: 10.1088/1361-6420/ae9c6c | Anahtar Kelimeler: inverse parabolic problem, final overdetermination, uniqueness, stability, Carleman estimate, mean field game — Özet: We consider
We consider inverse problems of determining a spatially varying coefficient or spatially varying factor in a source term from the initial and final data together and Cauchy data on a lateral boundary. We establish both uniqueness and the stability results. The key idea is a simple translation with respect to the time variable, which reduces the original inverse problems to well-studied inverse problems, for which standard Carleman estimates are applicable. Our research applies to a broad class of parabolic equations. We also discuss the uniqueness of determining spatially varying factors of source terms for a mean field game system.