AUTHORS: Gia Avalishvili, Mariam Avalishvili

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ABSTRACT: This paper is devoted to the construction and investigation of a hierarchy of two-dimensional models for thermoelastic piezoelectric plate with variable thickness, which may vanish on a part of the lateral boundary. The hierarchical two-dimensional models are constructed for plate consisting of inhomogeneous anisotropic thermoelastic piezoelectric material with regard to magnetic field, when density of surface force, and normal components of electric displacement, magnetic induction and heat flux vectors are given along the upper and the lower face surfaces of the plate. The boundary value problems corresponding to the constructed static two-dimensional models are investigated in suitable weighted Sobolev spaces. The relationship between the constructed two-dimensional models and the original three-dimensional one is investigated, and the convergence of the sequence of vector-functions of three variables restored from the solutions of the constructed two-dimensional problems to the solution of the original three-dimensional boundary value problem is proved and under additional conditions modeling error estimate is obtained

KEYWORDS: thermo-electro-magneto-elasticity, plates, two-dimensional models, boundary value problem, well-posedness, error estimate

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