Spatial behaviour of thermoelasticity with microtemperatures and microconcentrations

We consider a thermoelastic material with microtemperatures and microconcentrations. The mathematical model is represented by a system of partial differential equations with the coupling of the displacement, temperature, chemical potential, microconcentrations and microtemperatures fields. The processes of heat and mass diffusion play an important role in many engineering applications, such as satellite problems, manufacturing of integrated circuits or oil extractions. We study the spatial behaviour in a prismatic cylinder occupied by an anisotropic and inhomogeneous material. We impose final prescribed data that are proportional, but not identical, to their initial values. Moreover, we have zero body forces and zero lateral boundary conditions. The spatial behaviour is analysed in terms of some cross-sectional integrals of the solution that depend on the axial variable.