On the existence and decay in a new thermoelastic theory with two temperatures

Abstract

In this work, we study a new two-temperatures thermoelastic model. Both thermodynamic and conductive temperatures are included, being related by means of an elliptic or parabolic equation. Then two problems are considered assuming the dependence or not on the rate of conductivity temperature. Existence of solutions for the three-dimensional setting and the exponential energy decay in the one-dimensional case are shown.