On the well-posedness and stability of piezoelectric beams with magnetic effects, logarithmic damping, and Fourier-type thermal conduction

In this work, we study a magnetizable piezoelectric beam system with logarithmic damping and thermal effects governed by Fourier’s law of heat conduction. Such models are motivated by applications in smart materials and thermo-electro-mechanical structures, where the interplay of mechanical vibrations, electrical response, magnetic interactions, and heat dissipation plays a crucial role in stability analysis. First, we establish the well-posedness and investigate the asymptotic behavior of the system under this weak dissipation. Then, by employing the multiplier method together with the energy perturbation technique and suitable logarithmic inequalities, we establish a decay estimate without imposing additional restrictions on the structural parameters of the system. Our results demonstrate that the total energy decays to zero at a polynomial rate. To the best of our knowledge, this is the first result addressing the combined effects of logarithmic damping in magneto-thermo-piezoelectric beam systems, thereby extending and complementing earlier stability results obtained for piezoelectric beams with standard nonlinear damping.