Optimal Decay Rates for Kirchhoff Plates with Intermediate Damping

ABSTRACT

In this paper we study the asymptotic behavior of Kirchhoff plates with intermediate damping. The damping considered contemplates the frictional and the Kelvin-Voigt type dampings. We show that the semigroup those equations decays polynomially in time at least with the rate t ⁻¹ /(2−2θ ), where θ is a parameter in the interval [0, 1[. Moreover, we prove that this decay rate is optimal.

Keywords:
plate equation; polynomial decay; optimal decay; frictional damping; Kelvin-Voigt type damping