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On the linear theory of double porosity thermoelasticity under local thermal non-equilibrium

机译：局部热非平衡下双孔隙热弹性的线性理论

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摘要

In the present paper, the linear theory of thermoelasticity of double porosity materials under local thermal non-equilibrium is considered and the basic boundary value problems are investigated by using the boundary integral equation method (potential method). Indeed, the fundamental solution of system of steady vibrations equations of the considered theory is constructed explicitly by means of elementary functions and its basic properties are established. A Galerkin-type solution to this system of equations is presented and the completeness of this solution is proved. The basic internal and external boundary value problems of steady vibrations are formulated and the uniqueness theorems for classical solutions of these problems are proved. The basic properties of the surface and volume potentials and singular integral operators are established. Finally, the existence theorems for classical solutions of the above-mentioned boundary value problems are proved by using the potential method and the theory of singular integral equations.
机译：本文考虑了局部热不平衡条件下双孔隙材料热弹性的线性理论，并通过边界积分方程法（势能法）研究了基本边值问题。实际上，通过基本函数明确构造了所考虑理论的稳态振动方程组的基本解，并建立了其基本性质。给出了该方程组的Galerkin型解，并证明了该解的完整性。阐述了稳态振动的基本内，外边界值问题，并证明了这些问题的经典解的唯一性定理。建立了表面和体积电势的基本性质以及奇异积分算子。最后，利用势方法和奇异积分方程理论，证明了上述边值问题经典解的存在性定理。

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