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Abstract
This article concerns the derivation of a new potential theory for quasi-static problems of uncoupled thermoelasticity. The theory is based on a complete system of differential equations for a quasi-static problem of uncoupled thermoelasticity treated as a non-self-conjugate differential operator equation. To formulate a reciprocity theorem (Green's second identity), the conjugate system of differential equations is used. The reciprocity theorem is then employed to obtain a Somigliana-type formula. The boundary and initial properties of potentials in the Somigliana formula are studied for a homogeneous isotropic medium, and boundary integral equations for basic initial-boundary value problems are obtained.