Exponential stability analysis of a thermoelastic piezoelectric beam with delay effects under Cattaneo’s law

In the paper, we investigate a thermoelastic piezoelectric beam model with magnetic effects and delay term. The heat conduction of the system is governed by the Maxwell-Cattaneo law. Using the semigroup method, we first establish the well-posedness of the system. We then study the stability of the system in two different situations. In the absence of delay, we prove that the energy of the system decays exponentially, independently of the physical parameters of the system. Interestingly, in the more challenging case, when a delay is present in the first equation with no additional friction damping to absorb its destabilizing effects, we show that exponential stability is preserved, provided the delay coefficient is sufficiently small. Our stability result is obtained by carefully applying multiplier techniques with fewer auxiliary functionals compared to related problems in the literature.