Global well-posedness and general energy decay of solutions for fully dynamic and electrostatic piezoelectric beams with a viscoelastic damping

Abstract

In this article, we study a one-dimensional system of fully dynamic and electrostatic piezoelectric beams with a magnetic effect in the presence of a viscoelastic damping term acting on the mechanical equation. Under suitable assumptions on the kernel g, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations. And by constructing a suitable Lyapunov functional,
we establish a general energy decay result. Furthermore, our result does not depend on any relationship between system parameters.