Basic theorems in the equilibrium theory of thermoelasticity with microtemperatures

In this paper we consider the linear equilibrium theory of thermoelasticity with microtemperatures and some basic results of the classical theories of elasticity and thermoelasticity are generalized. The Green’s formulae in the considered theory are obtained. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) are proved. The representation of Galerkin type solution is obtained and the completeness of this solution is established. The formulae of integral representations of regular vector and regular (classical) solutions are obtained. The basic properties of thermoelastopotentials and singular integral operators are presented. Finally, the existence theorems for the internal and external basic BVPs are proved by means of the potential method and the theory of singular integral equations.