A domain of influence result about the time differential three-phase-lag thermoelastic model

This work represents a natural outlet of recent investigation about the well-posed question for the time differential three-phase-lag model of thermoelasticity. We deal with a cylindrical domain filled by an anisotropic and inhomogeneous thermoelastic material and assume that the initial-boundary data as well as the external supply terms that characterize the problem in concern are concentrated in a compact region of the considered volume. Within such a framework, we show the spatial behavior of the solutions in terms of existence of a domain of influence of the assigned data. We will remark that our results are obtained under restrictions involving the constitutive tensors and the delay times that are in complete agreement with the hypotheses that make the time differential three-phase-lag model thermodynamically consistent. The case of a semi-infinite cylindrical domain is also considered.