Asymptotic profiles for damped plate equations with rotational inertia terms.

We consider the Cauchy problem for plate equations with rotational inertia and frictional damping terms. We derive asymptotic profiles of the solution in L 2 -sense as t → ∞ in the case when the initial data have high and low regularity, respectively. Especially, in the low regularity case of the initial data one encounters the regularity-loss structure of the solutions, and the analysis is more delicate. We employ the so-called Fourier splitting method combined with the explicit formula of the solution (high-frequency estimates) and the method due to [R. Ikehata, Asymptotic profiles for wave equations with strong damping, J. Differential Equations257 (2014) 2159–2177.] (low-frequency estimates). In this paper, we will introduce a new threshold l ∗ : = n / 2 − 1 on the regularity of the initial data that divides the property of the corresponding solution to our problem into two parts: one is wave-like, and the other is parabolic-like. [ABSTRACT FROM AUTHOR]