Asymptotic Stability of Energy for a Weak Viscoelastic Plate Equation with Complementary Frictional Damping

Abstract

We are concerned with asymptotic stability of energy for plate equations with vanishing viscoelastic dampings and complementary frictional dampings, where the internal viscoelastic dampings are assumed to be time-dependent. In terms of the relaxation function $$\theta (t)$$ and the coefficient $$\gamma (t)$$ of viscoelastic term, we obtain the decay rates for the plate equations’ energies. Since we do not need the viscoelastic damping coefficient to be bigger than a fixed positive number, which is required in previous investigations of the asymptotic stability of the plate equations’ energies, our decay theorems extend and improve essentially the existing decay results for the plate equations in both viscoelastic damping case and mixed-type damping case.