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The Fourier method in three-dimensional boundary-contact dynamic problems of elasticity. (English) Zbl 0838.73012
Summary: The basic three-dimensional boundary-contact dynamic problems are considered for a piecewise-homogeneous isotropic elastic medium bounded by closed surfaces. Using the Fourier method, the considered problems are proved to be solvable under much weaker restrictions on the initial data as compared with other methods.

MSC:
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
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References:
[1] V.D. Kupradze, T.G. Gegelia, M.O. Basheleishvili, and T.V. Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. (Translated from Russian)North-Holland series in applied mathematics and mechanics, v. 25,North-Holland Publishing Company, Amsterdam-New York-Oxford, 1979; Russian original:Nauka, Moscow, 1976.
[2] D. G. Natroshvili and A. Ya. Jagmaidze, Dynamic problems of the classical theory of elasticity for piecewise-homogeneous bodies. (Russian)Tbilisi University Press, Tbilisi, 1978.
[3] K. Miranda, Partial equations of elliptic type. Translated from Italian into Russian)Inostrannaya Literatura, Moscow, 1957; Italian original:Springer-Verlag, Berlin, 1955.
[4] T. G. Gegelia, Some questions of the theory of multidimensional singular integral equations of the potential theory and their application in the theory of elasticity. (Russian)Dissertation for the Doctor of Science Degree, Tbilisi, 1963.
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