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The system of Lama's equations is investigated, describing the motion of theelastic media under subsonic, transonic and supersonic velocities of the movingsource of distributions, and its decisions in space of generalizedvector-functions. The questions are considered connected with arising shockwaves, which appear in ambience under supersonic source of distributions. Onbase of the generalized functions theories the method of the determination ofthe conditions on gaps of the decisions and their derivatives on shock wavesfronts is offered.

The generalized solutions of the Lama's equations in the case of running loads. The shock waves