Energy decay of a microbeam model with a locally distributed nonlinear feedback control

In this paper we address the problem of internal stabilization of the deflection of a microbeam, which is modeled by a sixth-order hyperbolic equation. Employing multiplier techniques and an integral inequality, we prove that a locally distributed nonlinear feedback control forces the energy associated to the deflection to decay exponentially or polynomially to zero. As a consequence of this, the deflection goes to the rest position as the time goes to infinity.