Applied Physics and Mathematics Annotation << Back INVERSE PROBLEMS FOR THE EQUATION OF THE VIBRATIONS OF THE BEAM IN FINDING THE SOURCE K.B. SABITOV In this work, for the equation of vibrations of a beam, inverse problems are studied for finding the right side (source of vibrations). The solutions of the problems are constructed in an explicit form as the sum of series and the corresponding theorems of uniqueness and existence are proved. When justifying the convergence of the series, the problem of small denominators arises. In this connection, estimates are established on separation from zero with the corresponding asymptotics. On the basis of these estimates, the convergence of series in the class of regular solutions of the beam equation is substantiated. Keywords: beam equation, initial conditions, boundary conditions, inverse problems, spectral method, series, uniqueness, existence. DOI: 10.25791/pfim.05.2020.1179 Pp. 36-38.