Inverse problems for coefficients of nonlinear differential equations arise in investigation of various processes in heat physics, physical chemistry, hydrogeology, nuclear physics, and other sciences. Usually these problems consist in determining a coefficient of an equation, the sought coefficient depending on the solution, basing on the additional information about the solution. A large number of papers are devoted to inverse problems of such a type; see, e.g., [1, 4, 5, 7]. Of much importance for analysis of such problems and development of numerical methods for their solution is the study of the uniqueness of their solution in classes of functions of finite smoothness. Theorems of uniqueness in such classes of functions were usually proved under the assumption that the sought coefficient is known for small values of the argument [2, 6, 9]. A method was first proposed in  making it possible to prove the uniqueness of the solution to an inverse problem on the whole and without the above-mentioned assumption. This method is applied in the present paper for study of the inverse problem for a nonlinear mathematical model of sorption dynamics with mixed-diffusional kinetics.