Polynomial stability of a Kirchhoff plate equation in the presence of a frictional damping, a fractional time delay, and a source term

Abstract

Abstract We investigate the asymptotic behavior of a Kirchhoff plate equation with free boundary conditions in a bounded domain of R 2 $\mathbb{R}^{2}$ . The model involves frictional internal damping, a time delay condition of fractional type and a source term. We derive a polynomial decay estimate for the associated semigroup by using the frequency domain method.

Keywords

• Kirchhoff plate
• Fractional delay
• Free boundary conditions
• Polynomial stability