Well-posedness and exponential stability of solutions for piezoelectric beams under magnetic, delay and thermodiffusion effects

Abstract

In this paper, we investigate the well-posedness and the asymptotic behavior of solutions to piezoelectric beams under magnetic, delay, and thermodiffusion effects. First, we establish the existence and uniqueness of solutions by applying semigroup theory. Then, using a perturbed energy method and constructing suitable Lyapunov functionals, we prove the exponential stability of the system.

Keywords

• Piezoelectric beams
• Magnetic effect
• Delay
• Thermodiffusion effects
• Semigroup approach
• Well-posedness
• Energy method
• Exponential stability

References

1. [1] M. Douib, Existence and exponential decay of solutions for magnetic effected piezoelectric beams with second sound and distributed delay term, Rend. Istit. Mat. Univ. Trieste 55 (1), 1-19, 2023.