The present work is an attempt to derive the representation of a Galerkin-type solution in the linear theory of generalized thermoelastic diffusion. First, the representation of a Galerkin-type solution of equations of motion is obtained in the form of a theorem. Then, the representation theorem of the Galerkin type of system of equations of steady oscillations is established. On the basis of this theorem, we finally establish a theorem which represents the general solution of the system of homogenous equations of steady oscillation in terms of metaharmonic functions.
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