Abstract
We consider a linear system of two coupled plate equations. One of these equations is conservative and the other has dissipative properties. Alabau et al. (J. Evol. Equ. 2:127–150, 2002) studied this kind of systems. In particular, they considered a system with frictional damping and have shown that, if both plates have the same elasticity/density ratio, the associated semigroup decays polynomially with the rate \(t^{-1/2}\). When the equations of this system have different elasticity/density ratio, the semigroup decays slower. Oquendo and Raya (Z. Angew. Math. Phys. 68:77, 2017) proved that the semigroup decays polynomially with the optimal rate \(t^{-1/4}\). When one of the equations of the coupled plates has the rotational inertia and a viscous damping the situation is completely different. In this work, we prove that no matter the elasticity/density relation, the rotational inertia forces the semigroup to decay polynomially with the optimal rate \(t^{-1/5}\).
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Suárez, F.M.S., Oquendo, H.P. Optimal Decay Rates for Partially Dissipative Plates with Rotational Inertia. Acta Appl Math 166, 131–146 (2020). https://doi.org/10.1007/s10440-019-00259-z
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DOI: https://doi.org/10.1007/s10440-019-00259-z