Uniqueness in an integral geometry problem and an inverse problem for the kinetic equation
Arif Amirov, Fikret Golgeleyen, Masahiro Yamamoto
article (Uluslararası, Hakemli) | Yazar(lar): Arif Amirov, Fikret Golgeleyen, Masahiro Yamamoto | Yıl: 2017 | Dergi/Kurum: APPLICABLE ANALYSIS | İndeks: WOS.SCI | DOI: 10.1080/00036811.2016.1213387 | Anahtar Kelimeler: Integral geometry problem, inverse problem, kinetic equation, uniqueness, 35R30, 53C65 — Özet: In thi
In this paper, we discuss the uniqueness in an integral geometry problem along the straight lines in a strongly convex domain. Our problem is related with the problem of finding a Riemannian metric by the distances between all pairs of the boundary points. For the proof, the problem is reduced to an inverse source problem for a kinetic equation and then the uniqueness theorem is proved using the tools of Fourier analysis.