In this paper we study the questions of the existence and uniqueness of the solutions for a thermoelastic system of equations in a two-dimensional domain, where both the viscosity v and the rigidity D are positive. It seems that such a system has up to now been considered in a one-dimensional setting only. The change of dimensions enforces the growth conditions with respect to θ and the additional regularity of the data. The existence of solutions in the case of the Neumann boundary conditions for θ and some weak regularity of data is proved. Under stronger regularity conditions the uniqueness is also established. The system has an interpretation as a plate reinforced by a shape memory alloy (SMA) wire mesh.
