DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION
DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION
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DOI：
10.1142/s0218202511500126
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发表时间：
2012-02
影响因子：
3.5
通讯作者：
Yongqing Liu;S. Kawashima
中科院分区：
文献类型：
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作者：
Yongqing Liu;S. Kawashima
本文考虑了具有记忆项的Repubshenko系统的初值问题。利用Fourier-Laplace变换构造基本解，得到了问题的求解公式。此外，利用Fourier空间中的能量方法，我们得到了解在Fourier空间中的逐点估计，它给出了解的一个锐衰减估计。结果表明，该系统的衰减性质是正则性损失型的，比具有摩擦耗散的Kashshenko系统的衰减性质弱。
In this paper we consider the initial value problem for the Timoshenko system with a memory term. We construct the fundamental solution by using the Fourier–Laplace transform and obtain the solution formula of the problem. Moreover, applying the energy method in the Fourier space, we derive the pointwise estimate of solutions in the Fourier space, which gives a sharp decay estimate of solutions. It is shown that the decay property of the system is of the regularity-loss type and is weaker than that of the Timoshenko system with a frictional dissipation.