Open Access Research

A generalization on the solvability of integral geometry problems along plane curves

Zekeriya Ustaoglu

Author Affiliations

Department of Mathematics, Bulent Ecevit University, Zonguldak, 67100, Turkey

Boundary Value Problems 2013, 2013:202  doi:10.1186/1687-2770-2013-202

Published: 8 September 2013

Abstract

This paper is concerned with a general condition for the solvability of integral geometry problems along the plane curves of given curvatures. As two important results, the solvabilities of integral geometry problems along the family of circles with fixed radius and along the family of circles of varying radius centered on a fixed circle are given. By using some extension of the class of unknown functions, the proofs are based on the solvabilities of equivalent inverse problems for transport-like equation.

MSC: 35R30, 53C65, 65N30.

Keywords:
integral geometry problem; inverse problem; Galerkin method; transport-like equation