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Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts. II |
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| Authors: | R Duduchava D Natroshvili E Shargorodsky |
| Institution: | (1) A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, Z. Rukhadze Str., 380093 Tbilisi, Republic of Georgia;(2) Department of Mathematics, Georgian Technical University, (99) 77, M. Kostava Str., 380075 Tbilisi, Republic of Georgia;(3) Department of Mechanics and Mathematics, Tbilisi State University, 2, University Str., 380043 Tbilisi, Republic of Georgia |
| Abstract: | In the first part 1] of the paper the basic boundary value problems of the mathematical theory of elasticity for three-dimensional anisotropic bodies with cuts were formulated. It is assumed that the two-dimensional surface of a cut is a smooth manifold of an arbitrary configuration with a smooth boundary. The existence and uniqueness theorems for boundary value problems were formulated in the Besov
and Bessel-potential (
p
s
) spaces. In the present part we give the proofs of the main results (Theorems 7 and 8) using the classical potential theory and the nonclassical theory of pseudodifferential equations on manifolds with a boundary. |
| Keywords: | 35C15 35S15 73M25 |
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