Abstract
In this work, we consider a one-dimensional linear thermoelastic shear beam model coupled with a heat equation, where the heat conduction is given by the generalized dual-phase-lag model. We establish the well-posedness of the system by using the semigroup theory. Then, the exponential stability is obtained by applying the Gearhart–Herbst–Prüss–Huang theorem under the hypothesis
2
τ
θ
>
τ
q
. In addition, we conduct several numerical tests to illustrate our theoretical results.