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The system of Lama’s equations is investigated, describing the motion of the elastic media under subsonic, transonic and supersonic velocities of the moving source of distributions, and its decisions in space of generalized vector-functions. The questions are considered connected with arising shock waves, which appear in ambience under supersonic source of distributions. On base of the generalized functions theories the method of the determination of the conditions on gaps of the decisions and their derivatives on shock waves fronts is offered.

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