Differential operators associated with the equations of motion and nondissipative heat conduction in the Green-Naghdi theory of thermoelasticity

We consider a wave (hyperbolic) heat conduction theory of the Green-Naghdi type. In the framework of the continual approach, such a theory permits describing low-temperature phenomena of quantum nature (for example, the second sound effect) that are not within reach of the classical parabolic thermoelasticity. At low temperatures, the medium heat conductivity experiences a substantial increase, which should be reckoned with in the design and analysis of cryogenic devices. This change in heat conduction properties results from the wave character of heat propagation, which cannot be taken into account in classical heat conductivity models of the diffusion type but can be described by hyperbolic models of the Green-Naghdi type. That is why considerable attention has been paid to the development of hyperbolic heat conduction models. The present paper deals with analytic solution methods for the corresponding nonself-adjoint initial-boundary value problems.