Uniform Decay for Thermoelastic Diffusion Problem of Type III with Delays

In this article, we consider a thermoelastic diffusion problem of type III in one space dimension with boundary constant delays. First we prove that the one-dimensional problem is well-posed by the semigroup theory. By introducing a suitable energy and an appropriate Lyapunov functional, we show under smallness conditions that the damping delay effect through heat and mass diffusion conduction is strong enough to uniformly stabilize the system. Moreover, our results can be extended to the case where our system is subjected to other damping functions as the time-varying delay or the distributed delay.