Abstract
The goal of this work is to demonstrate the exponential stability of a recently proposed thermoelastic theory called the improved dual-phase-lag (IDPL) model given by Zarei and Pilla (2023), precisely to address the encounters posed by fast and ultrafast heating of materials. In order to obtain it, we consider the one-dimensional problem of the theory of thermoelasticity with an IDPL model. Then, using the Routh-Hurwitz criterion, we prove that when τ0 < τ1, the solutions are obtained exponentially stable, and when τ0 < τ1, there exist unstable solutions.