Inverse Problem for an Equation of Mixed Parabolic–Hyperbolic Type with a Bessel Operator

For an equation of the mixed parabolic–hyperbolic type with a Bessel operator, we study the inverse problem associated with the search for the unknown right-hand side. By separation of variables, the problem is reduced to solving ordinary differential equations for the coefficients of the Fourier–Bessel series expansions of the unknown functions in orthonormal Bessel functions of the first kind and zero order. A criterion for the uniqueness and existence of a solution of the problem is established.

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