Problems of elastic wave scattering by various types of inhomogeneities rank among the most complex and relevant topics in the field of deformable solid dynamics. From an applied perspective, this is due to the fact that information about the dynamic stress–strain state in the vicinity of such inhomogeneities is of significant interest for various engineering and physical applications.

The objective of this study is to investigate the nonstationary scattering of elastic waves by a spherical inclusion embedded in an infinite elastic medium. The analytical approach to the solution involves the application of Fourier integral transforms with respect to time. It
is established that the eigenfunctions of the considered problem cannot be treated as vectors in a Hilbert space, since they are not square-integrable due to their exponential growth with distance. This necessitates the use of generalized functions and specialized methods from scattering theory.