A domain of influence in the Moore–Gibson–Thompson theory of dipolar bodies

We establish a domain of influence theorem for the mixed initial-boundary value problem in the context of the Moore–Gibson–Thompson theory of thermoelasticity for dipolar bodies. Based on the data of the mixed problem, we define, for a finite time t>0, a bounded domain $B_t $ and prove that the displacements and the temperature decrease to zero, outside of the domain $B_t $. The main result is obtained with the help of two auxiliary results, namely two integral inequalities. We managed to prove that this type of influence domain can be built even if it is considered in a much more complex context. Thus, compared to the classical context in which this concept appeared, we took into account the heat conduction principle from the Moore–Gibson–Thompson theory, we considered the thermal effect and we analyzed the effect of the dipolar structure of the environment.