The third boundary value problem for the system of equations of linear thermoelasticity

The existence and uniqueness of a generalized solution are proved for the third boundary value problem for a system of differential equations in the linear thermoelasticity theory. The displacement vector and temperature of the medium are the sought functions. The existence of a solution is proved, using the contraction mapping principle. In obtaining some necessary a priori estimates, the expansion of the solution was used in a series of generalized eigenfunctions of the Laplace operator.