An inverse source problem for the Schrodinger equation with variable coefficients by data on flat subboundary
Fikret Golgeleyen, Ismet Golgeleyen, Masahiro Yamamoto
article (Uluslararası, Hakemli) | Yazar(lar): Fikret Golgeleyen, Ismet Golgeleyen, Masahiro Yamamoto | Yıl: 2024 | Dergi/Kurum: JOURNAL OF MATHEMATICAL PHYSICS | İndeks: WOS.SCI | DOI: 10.1063/5.0087112 — Özet: We consider an inverse source problem for the Schrodinger equation with variable coefficients. We prove the u
We consider an inverse source problem for the Schrodinger equation with variable coefficients. We prove the uniqueness of solution of the problem by data on a flat subboundary over time interval, under a certain condition of the coefficients of the principal terms. We first reduce the inverse problem to a Cauchy problem for a system of integro-differential equations by using Fourier transform. Next, we establish a pointwise Carleman type inequality which is the key tool in the proof of our main result.