Uniqueness in an Integral Geometry Problem and an Inverse Problem for the Kinetic Equation
| Autor: | Fikret Gölgeleyen, Masahiro Yamamoto, Arif Amirov |
|---|---|
| Přispěvatelé: | Zonguldak Bülent Ecevit Üniversitesi |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Mathematics - Differential Geometry
Applied Mathematics 010102 general mathematics Mathematical analysis Boundary (topology) uniqueness kinetic equation Inverse problem 01 natural sciences Elliptic boundary value problem Integral geometry 010101 applied mathematics Integral geometry problem 53C65 65M32 Uniqueness theorem for Poisson's equation Differential Geometry (math.DG) Inverse scattering problem Free boundary problem FOS: Mathematics inverse problem Uniqueness Mathematics::Differential Geometry 0101 mathematics Analysis Mathematics |
| Popis: | 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. © 2016 Informa UK Limited, trading as Taylor & Francis Group. University of Tokyo: 15H05740 Japan Society for the Promotion of Science Most part of the paper has been written during the stay of the second-named author at Department of Mathematical Sciences of The University of Tokyo and the stay was supported by the program ?Leading Graduate Course for Frontiers of Mathematical Sciences and Physics?. The third-named author is supported by Grant-in-Aid for Scientific Research (S) 15H05740 of Japan Society for the Promotion of Science. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|