Otar Chkadua, Anika Toloraia

Mixed Type Transmission Dynamical Problems with Interior Cracks of the Thermo-Piezo-Electricity Theory Without Energy Dissipation

abstract:
In the paper, we study a mixed type interaction dynamical problem with interior cracks between thermo-elastic and thermo-piezoelastic bodies. The model under consideration is based on the Green-Naghdi theory of thermo-piezoelectricity without energy dissipation. This theory allows the thermal waves to propagate only with a finite speed. Using the Laplace transform, potential theory and the method of boundary pseudodifferential equations, we prove the existence and uniqueness of solutions and analyze their smoothness.

Mathematics Subject Classification: 35B65, 35S15, 47G30, 74A15, 74F05, 74F15, 74G40

Key words and phrases: Thermo-piezoelectricity without energy dissipation, bodies with microstructure, transmission problem, potential method, pseudodifferential equations