Stability of non-classical thermoelasticity mixture problems

Abstract

We discuss the stability problem for binary mixtures systems coupled with heat equations. The present manuscript covers the non-classical thermoelastic theories of Coleman-Gurtin and Gurtin-Pipkin - both theories overcome the property of infinite propagation speed (Fourier's law property). We first state the well-posedness and our main result is related to long-time behavior. More precisely, we show, under suitable hypotheses on the physical parameters, that the corresponding solution is stabilized to zero with exponential or rational rates.