Continuous dependence in thermopiezoelectricity of nonsimple materials

In this paper, we consider the linear theory for a model of a thermopiezoelectric nonsimple body as presented in Passarella and Tibullo (Entropy, https://doi.org/10.3390/e24091229. 2022) in which the second displacement gradient and the second electric potential gradient are included in the set of independent constitutive variables, adopting an entropy production inequality model proposed by Green and Laws. We set a mixed initial-boundary value problem and starting from two solutions we establish a reciprocity relation for the general case, which extends the analogue in Ciarletta et al. (Mech Res Commun, https://doi.org/10.1016/j.mechrescom.2022.103969, 2022), and two continuous dependence theorems for centrosymmetric materials. Both theorems consider the difference of two solutions of the problem: the first one depends only from supply terms, which are the external body forces, electric charge density and heat supply and the second one only depends from initial data for displacement, velocity, relative temperature and entropy fields. All these data, together with the boundary conditions, are assigned.