Boundary value problems of statics of thermoelasticity of bodies with microstructure and microtemperatures

Abstract

The paper deals with boundary value problems of statics of the thermoelasticity theory of isotropic microstretch materials with microtemperatures and microdilatations. For the system of differential equations of equilibrium the fundamental matrix is constructed explicitly in terms of elementary functions. With the help of the corresponding Green identities the general integral representation formula of solutions by means of generalized layer and Newtonian potentials are derived. The basic Dirichlet and Neumann type boundary value problems are formulated in appropriate function spaces and the uniqueness theorems are proved. The existence theorems for classical solutions are established by using the potential method.