Fourier或Cattaneo定律下含界面滑移的Cauchy热弹性层合板Reynshenko问题的新衰减率
New decay rates for a Cauchy thermelastic laminated Timoshenko problem with interfacial slip under Fourier or Cattaneo laws
摘要：
本文的目的是研究具有界面滑移的层合梁在整个空间R中受仅作用于一个由Fourier或Cattaneo定律建模的分量上的热效应的解的衰减。当热效应通过层合梁的第二或第三分量（转角位移或滑移动力）起作用时，我们得到了两个系统，Roshenko-Fourier和Roshenko-Cattaneo系统，在解及其高阶导数关于空间变量的L2范数下满足相同的多项式稳定性估计.衰减率取决于初始数据的规律性。此外，正则性损失型性质的存在与否取决于系统参数之间的某种关系。然而，当热效应是通过系统的第一分量（横向位移），一个新的稳定性条件，介绍了两个Eschhenko-Fourier和Eschhenko-Cattaneo系统。该稳定性条件是多项式稳定性和收敛到零之间的阈值的形式。为了证明我们的结果，我们使用的能量方法在傅立叶空间结合明智的选择的权函数，以建立适当的李雅普诺夫泛函。
英文摘要：
The objective of the present paper is to investigate the decay of solutions for a laminated Timoshenko beam with interfacial slip in the whole space R subject to a thermal effect acting only on one component modelled by either Fourier or Cattaneo law. When the thermal effect is acting via the second or third component of the laminated Timoshenko beam (rotation angle displacement or dynamic of the slip), we obtain that both systems, Timoshenko-Fourier and Timoshenko-Cattaneo systems, satisfy the same polynomial stability estimates in the L2 -norm of the solution and its higher order derivatives with respect of the space variable. The decay rate depends on the regularity of the initial data. In addition, the presence and absence of the regularity-loss type property are determined by some relations between the parameters of systems. However, when the thermal effect is acting via the first comoponent of the system (transversal displacement), a new stability condition is introduced for both TimoshenkoFourier and Timoshenko-Cattaneo systems. This stability condition is in the form of threshold between polynomial stability and convergence to zero. To prove our results, we use the energy method in Fourier space combined with judicious choices of weight functions to build appropriate Lyapunov functionals.
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