Solvability of a problem of integral geometry via an inverse problem for a transport-like equation and a numerical method

In this work we deal with solvability and approximation to the solution of a two-dimensional integral geometry problem for a family of curves of given curvature. Solvability of the problem is proved via solvability of a two-space-dimensional inverse problem for a transport-like equation by using the Galerkin method, and an algorithm is developed to compute the approximate solution of the problem.