Decay property of Timoshenko system in thermoelasticity
Decay property of Timoshenko system in thermoelasticity
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DOI：
10.1002/mma.1569
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发表时间：
2012-02
影响因子：
2.9
通讯作者：
B. Said-Houari;A. Kasimov
中科院分区：
文献类型：
--
作者：
B. Said-Houari;A. Kasimov
本文研究了在Fourier和Cattaneo热传导定律下，热弹性力学中的一个Reynshenko系统在整个空间中的衰减性质。我们指出，虽然傅立叶定律中固有的无限传播速度的悖论通过改变为卡塔内奥定律而消除，但后者总是导致具有规律性损失型衰减性质的解。用来证明我们的结果的主要工具是能量方法在傅立叶空间与一些积分估计。我们导出了解的L2衰减估计，并观察到，对于傅立叶定律，如果系统中第一和第二方程的波速不同，则解的衰减结构是正则性损失型的。对于卡塔内奥定律，无论波速如何，都会发生规则性损失类型的衰减特性。此外，通过将初始数据限制为U 0 ∈Hs（R）<$L1，γ（R）具有适当大的s和γ ∈ [0，1]，我们可以得到更快的衰变估计，衰变率提高了t−γ/2倍。版权所有© 2011约翰威利父子有限公司.
We investigate the decay property of a Timoshenko system of thermoelasticity in the whole space for both Fourier and Cattaneo laws of heat conduction. We point out that although the paradox of infinite propagation speed inherent in the Fourier law is removed by changing to the Cattaneo law, the latter always leads to a solution with the decay property of the regularity‐loss type. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We derive L2 decay estimates of solutions and observe that for the Fourier law the decay structure of solutions is of the regularity‐loss type if the wave speeds of the first and the second equations in the system are different. For the Cattaneo law, decay property of the regularity‐loss type occurs no matter what the wave speeds are. In addition, by restricting the initial data to U0∈Hs(R)∩L1,γ(R) with a suitably large s and γ ∈ [0,1], we can derive faster decay estimates with the decay rate improvement by a factor of t−γ/2. Copyright © 2011 John Wiley & Sons, Ltd.