Inverse problem for an equation of mixed parabolic-hyperbolic type with a Bessel operator

In this work, for an equation of mixed parabolic-hyperbolic type with a Bessel operator, we study the inverse problem associated with the search for an unknown right-hand side. On based method separation of variables, the problem is reduced to solving an ordinary differential equations with respect to the coefficients of the Fourier—Bessel expansion of unknown functions in orthonormal Bessel functions of the first kind of zero order. A criterion for the uniqueness and existence of a solution to the stated problem is established.