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Mixed Crack Type Problem in Anisotropic Elasticity
Author(s) -
Duduchava R.,
Natroshvili D.
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981910105
Subject(s) - mathematics , uniqueness , mathematical analysis , boundary value problem , elasticity (physics) , neumann boundary condition , anisotropy , mixed boundary condition , type (biology) , dirichlet distribution , vector valued function , ecology , materials science , physics , quantum mechanics , composite material , biology
Abstract The paper deals with three‐dimensional mixed boundary value problem of the anisotropic elasticity theory when the elastic body under consideration has a cut in the form of an arbitrary non‐closed, two‐dimensional, smooth surface with a smooth boundary: on one side of the cut surface the Dirichlet type condition (i.e., the displacement vector) is given, while on the other side the Neumann type condition (i.e., the stress vector) is prescribed. Applying the potential method and invoking the theory of ΨDEs uniqueness, existence and regularity results are proved in various function spaces. The asymptotic expansion of the solution of the corresponding system of boundary ΨDEs is written.