On an Euclidean plane with coordinates (x, y), a closed bounded region M with a smooth boundary ∂M and metrics g of form ds ² = e^2μ(x,y) (dx ²+ dy ²) (μ = μ(x,y) ∈ C∞ (M)) is considered. The inverse problem of recovering functions u = u(x,y,θ) ∈ C ⁴(ΩM) and f _i = f _i(x,y) ∈ C ³(M), i = 0, 1, 2, 3, 4, which satisfy an kinetic equation and boundary conditions is investigated.

The solution non-uniqueness set is described. The functions u and f _i in (1) are proved to be uniquely defined by a proper choice of some three differentiable functions.