Boundary value problems of the quasi-static theory of thermoviscoelasticity of binary mixtures

The boundary value problems (BVPs) of the quasi-static theory of thermoviscoelasticity of binary mixtures are investigated. Indeed, the fundamental solution of the systems of quasi-statics equations in the considered theory is constructed and its basic properties is established. The Green’s formulae are obtained and the uniqueness theorems of solutions of the BVPs of quasi-statics are proved. The basic properties of surface and volume potentials are established and the BVPs are reduced to the singular integral equations. The symbolic determinant of the corresponding operators are calculated explicitly. The existence theorems of the classical solutions of the BVPs of quasi-statics in the considered theory are proved by using potential method and the theory of singular integral equation.