On the Thermal Theory of Micropolar Solid-Fluid Mixture

In this paper we study the linear thermal theory of the micropolar solid-fluid mixtures. We consider a mixture consisting of an isotropic micropolar solid and a compressible fluid. First, we establish estimates of Saint-Venant type for bounded bodies in terms of two appropriate time-weighted surface power functions. An alternative estimate of Phragmen-Lindelof type for unbounded bodies is also presented. Further, for unbounded bodies we are able to establish an estimate which proves that the measure associated with the solution decays faster than an exponential of a second degree polynomial, provided an appropriate class of mixtures is considered. This estimate shows that at large distance from the support of the external given data, the spatial decay of processes is influenced only by the thermal effect and by the viscosities of the fluid.