Uniqueness theorems in the steady vibration problems of the Moore–Gibson–Thompson thermoporoelasticity

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Abstract In this paper, the linear model of Moore–Gibson–Thompson thermoporoelasticity is considered and the governing equations of motion and steady vibrations are given. The basic system of equations of steady vibrations with respect to the displacement vector, the changes of temperature and fluid pressure are proposed. Then the radiation conditions are established and Green’s first identity is obtained. Finally, on the basis of this identity, the uniqueness theorems for classical solutions of the boundary value problems of steady vibrations in the theory of MGT thermoporoelaticity are proved.