NEW DECAY RATES FOR A PROBLEM OF PLATE DYNAMICS WITH FRACTIONAL DAMPING

Abstract

In this paper, we obtain decay rates for the total energy associated to the linear plate equation with effects of rotational inertia and a fractional damping term depending on a number θ ∈ [0, 1]. We observe that the dissipative structure of the equation with θ = 0 is of the regularity-loss type. This decay structure still remains true in the plate equation with a power of fractional damping θ > 0, but it becomes more weak when θ increase. This means that we can have an optimal decay estimate of solutions under an additional regularity assumption on the initial data. Our results generalize previous results by Luz and Charão and some of recent results due to Sugitani and Kawashima. We use a special method in the Fourier space which we developed in a previous work for the wave equation. So, our approach shows to be very effective to study decay properties for several problems in Rn.