非线性阻尼热弹性系统的下界和最优性
Lower Bound and optimality for a nonlinearly damped Timoshenko system with thermoelasticity
摘要：
本文研究了一类热弹性非线性振动系统的二次振动问题。我们首先研究了这个系统的强稳定性，然后利用\cite{2}（也见\cite{alabau}）中引入的能量比较原理得到了系统的强低能估计.这些结果的主要优点之一是，它们使我们能够证明在\cite{ali}中得到的渐近结果（如$t\rightarrow \infty$）的最优性。我们还将\cite{alabau}中关于非线性阻尼热弹性系统的良好结果推广到我们的模型中。我们的结果的最优性也通过一些显式的非线性阻尼项的例子进行了研究。我们的结果的证明依赖于\cite{AB1, AB2}中的方法。
英文摘要：
In this paper, we consider a vibrating nonlinear Timoshenko system with thermoelasticity with second sound. We first investigate the strong stability of this system, then we devote our efforts to obtain the strong lower energy estimates using Alabau--Boussouira's energy comparison principle introduced in \cite{2} (see also \cite{alabau}). One of the main advantages of these results is that they allows us to prove the optimality of the asymptotic results (as $t\rightarrow \infty$) obtained in \cite{ali}. We also extend to our model the nice results achieved in \cite{alabau} for the case of nonlinearly damped Timoshenko system with thermoelasticity. The optimality of our results is also investigated through some explicit examples of the nonlinear damping term. The proof of our results relies on the approach in \cite{AB1, AB2}.
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