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Three general, complete solutions of a coupled hyperbolic or hyperbolic-parabolic system of two second-order linear partial differential equations are presented. The system includes among its particular cases the governing field equations of the conventional as well as generalized thermoelasticity theories. The solutions obtained are analogous to the Lame, Papkovitch, and Galerkin solutions in classical elasticity. The interrelationships among the solutions are also exhibited. Some solutions obtained in earlier works are deduced as special cases of the unified solutions obtained here.

Complete solutions of a coupled system of partial differential equations arising in thermoelasticity