New decay rates for a problem of plate dynamics with fractional damping.
New decay rates for a problem of plate dynamics with fractional damping.
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具有分数阻尼的板动力学问题的新衰减率。
DOI：
10.1142/s0219891613500203
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
C. R. da Luz and Ryo Ikehata
中科院分区：
文献类型：
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作者：
R. C. Charao;C. R. da Luz and Ryo Ikehata
本文得到了具有转动惯量和分数阶阻尼项的线性板方程的总能量随θ ∈ [0，1]的衰减率。我们观察到当θ = 0时方程的耗散结构是正则-损失型的。这种衰减结构在分数阻尼幂次θ > 0时仍然成立，但随着θ的增大而减弱。这意味着我们可以在初始数据的额外正则性假设下得到解的最优衰减估计。我们的结果推广了Luz和Charão的已有结果以及Sugitani和Kawashima的一些近期结果。我们使用一种特殊的方法在傅立叶空间，我们在以前的工作中开发的波动方程。因此，我们的方法是非常有效的研究衰减性质的几个问题在Rn。
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 inRn.