Some theorems in the generalized theory of thermo-magnetoelectroelasticity under Green-Lindsay's model

This paper is concerned with the generalized theory of thermo-magnetoelectroelasticity in the frame of Green-Lindsay's model which permits the propagation of waves at a finite speed. First, we establish a reciprocity relation which involves thermoelastic processes at different instants. Then we show that this relation can be used to obtain reciprocity, uniqueness, and continuous dependence theorems. The reciprocity theorem avoids both the use of the Laplace transform and the incorporation of initial conditions into the equations of motion. The uniqueness theorem is derived avoiding both the use of the definiteness assumption on the elasticity tensor and the restriction that the conductivity tensor is positive definite. We prove also that the reciprocity relation leads to a continuous dependence theorem studied on external loads and heat supply and initial data, which ensures that the mathematical model for the generalized problem is well posed.