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The basic three-dimensonal boundary-contact dynamic problems are considered for a piecewise-homogeneous isotropic elastic medium bounded by several closed surfaces. Using the Fourier method, the considered problems are proved to be solvable under much weaker restrictions on the initial data of the problems as compared with other methods. 1991 Mathematics Subject Classification. 73B30, 73C25. Key words and phrases. Fourier method, boundary-contact dynamic problems of elasticity, classicaldoi:10.1007/bf02262854 fatcat:botvxs3ikje53fnbf6s67l7rtm