EXISTENCE RESULT AND EXPONENTIAL DECAY FOR A THERMOELASTIC SYSTEM WITH WENTZELL / ACOUSTIC BOUNDARY CONDITIONS TYPE

<div> In this paper, we consider the linear thermoelastic system defined on a bounded domain Ω ⊂ R 3 with smooth boundary Γ = Γ 0 ∪Γ 1 . Under suitable conditions on Γ and the function a(x), we establish the well-posedness and exponential stability of the system using semigroup theory and the multiplier method, respectively. Our results are achieved without introducing an additional damping term in the impenetrability condition. The main finding demonstrates that interior localized damping a(x)u ′ , applied only on a subset ϑ of the domain Ω, is sufficient to stabilize the entire system. </div>