Boundary-value Problems of Piezoelectricity in Domains with Cuts
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چکیده
In a domain with cut static boundary-value problems of piezoelectricity are investigated. The existence and uniqueness of solutions of the considered boundary value problems are proved and an asymptotic expansion of solutions near the edges of the cut are obtained. Let Ω and Ω1 (Ω1 ⊂ Ω) be a bounded domains in the three-dimensional Euclidean space R with infinitely smooth boundaries ∂Ω and ∂Ω1, respectively. We assume that the boundary ∂Ω1 of the domain Ω1 is the union of two surfaces: ∂Ω1 = S ∪ S0, and that the boundary ∂S = ∂S0 is an infinitely smooth curve. Denote Ω2 = Ω\Ω1. We suppose that the domain Ω\S is filled with an anisotropic homogeneous piezoelectric material having a cut at S . In the domain Ω\S, let us consider the system of static equations of piezoelectricity for a homogeneous anisotropic medium [1]:
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