Thermo-elastic and thermo-piezo-elastic interaction crack type boundary-transmission problems with regard to the microrotation (Q6579338)

The authors study a boundary-transmission problem for a composed elastic structure consisting of two contacting bodies occupying two three-dimensional adjacent regions with a common contacting interface, being a proper part of the boundaries of the adjacent regions. The mathematical model, which takes into account coupling effects between thermo-mechanical and electric fields in elastic composites, is based on the Green-Naghdi theory of thermo-piezo-electricity without energy dissipation. This theory permits the thermal waves to propagate only with a finite speed. The system of partial differential equations of pseudo-oscillations is obtained from the corresponding dynamical model by the Laplace transform. Using the potential theory and the method of pseudodifferential equations on manifolds with a boundary, the authors prove the existence, uniqueness and regularity of solutions.