Uniqueness in an integral geometry problem and an inverse problem for the kinetic equation

作者：Amirov Arif; Golgeleyen Fikret; Yamamoto Masahiro^*

来源：APPLICABLE ANALYSIS, 2017, 96(13): 2236-2249.

DOI：10.1080/00036811.2016.1213387

• Integral geometry problem
• inverse problem
• kinetic equation
• uniqueness
• 35R30
• 53C65

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.

• 出版日期2017