A domain of influence theorem for thermoelasticity without energy dissipation

Abstract

The present work is concerned with the thermoelasticity theory of Green and Naghdi of type I, II and III. By considering a mixed initial-boundary value problem for an isotropic medium in the context of all three models of type I, II and III in a unified way, we derive an identity in terms of the temperature and potential. On the basis of this identity, we establish the domain of influence theorem for the Green–Naghdi-II model. This theorem implies that for a given bounded support of thermomechanical loading, the thermoelastic disturbance generated by the pair of temperature and potential of the system vanishes outside a well-defined bounded domain. This domain is shown to depend on the support of the load, that is, on the initial and boundary data. It is also shown that under Green–Naghdi-II model, the thermoelastic disturbance propagates with a finite speed that is dependent on the thermoelastic parameters.

A domain of influence theorem under MGT thermoelasticity theory

“…In the three phase-lag model, the domain of influence theorem has been derived by Kumar and Kumar [39]. Domain of influence theorems under the type-II thermoelasticity theory are reported by Kumari and Mukhopadhyay [40, 41]. The domain of influence results for a natural stress–heat-flux problem under the MGT thermoelasticity theory have been recently discussed by Jangid and Mukhopadhyay [42].…”