Dynamic linear viscoelasticity problems for piecewise homogeneous bodies

We consider problems on transient wave processes in linearly viscoelastic piecewise homogeneous bodies in the case of small strains, a bounded perturbation propagation domain, and bounded creep of the materials forming the homogeneous components of the bodies. We study problems related to the construction of solutions of such problems by the method of Laplace integral transform with respect to time and the subsequent inversion. We state assertions about the properties of Laplace transforms of the solutions, which simplify the process of determining the original functions. We also consider relations of correspondence between relaxation kernels that belong to different function classes but still affect transient wave processes in a similar way.