Exponential Decay Results of Solutions for a One‐Dimensional Magnetizable Piezoelectric Beam System of Thermoelasticity of Type III With Strong Damping and a Strong Delay

ABSTRACT In this research work, we study a one‐dimensional magnetizable piezoelectric beam system with strong damping and a strong delay acting on the heat equation, where the heat conduction is given by Green and Naghdi theory. First, we establish by exploiting the semigroup theory that the system is well‐posed. Through the construction of an appropriate Lyapunov functional, we establish the exponential stability result for the solutions of the system. The exponential stability of the system's solutions is established under a pertinent assumption regarding the weight of the delay. This assumption posits that the damping effect through heat conduction is sufficiently potent to stabilize the system, even when a time delay is introduced. Importantly, the robustness of our result is noteworthy, as it does not hinge on any specific relationships among system parameters.