In physical applications, there are many inverse problems associated with differential and integro-differential equations in partial derivatives in bounded and unbounded domains. In this connection, in this paper, we study a singularly perturbed inverse Kac-Boltzmann type problem [1] in an unbounded domain with a priori information. Moreover, a condition is established for the solvability and proximity of solutions of the singularly perturbed inverse problem and the degenerate inverse problem in the weight Hilbert space [9].

inverse problem, transfer problems, weight space, singularly perturbed equation (SPE), prior information.