Inverse Transforms of Operational Images in Mathematical Models of Generalized Problems for Hyperbolic-Type Equations

Consideration has been given to a series of operational (after Laplace) nonstandard images whose inverse transforms are absent from the existing operational-calculus handbooks. The indicated images are involved in operational solutions to a wide class of generalized boundary-value problems based on hyperbolic-type equations that take account of the finite velocity of propagation of physical-field potentials, and also in solutions to the problems of hydrodynamics, vibration theory, and thermomechanics that have been obtained with account of the relaxation properties of a medium. New equivalent analytical solutions to generalized boundary-value problems for a partially bounded domain have been obtained. The presented relations can be used for constructing mathematical models of diverse external actions on materials.