Decay property of the Timoshenko–Cattaneo system
Decay property of the Timoshenko–Cattaneo system
复制标题
TimoshenkoâCattaneo 系统的衰变特性
DOI：
10.1142/s0219530515500062
复制
发表时间：
2015
影响因子：
2.2
通讯作者：
S. Kawashima
中科院分区：
文献类型：
--
作者：
N. Mori;S. Kawashima
本文研究一维全空间中具有Cattaneo型热传导的Koshenko系统。我们研究了系统的耗散结构，并在一般情况下得到了解的最优衰减估计。我们的衰减估计是基于详细的逐点估计的解决方案在傅立叶空间。我们观察到，我们的Eschenko-Cattaneo系统的衰变性质是正则性损失型。这种衰减性质与耗散的Kazhenko系统的衰减性质略有不同（见[K. Ide，K. Haramoto和S. Kawashima，Decay properties of regularity-loss type for dissipative Rehshenko system，Math. Models Methods Appl.Sci.18（2008）647-667]）。然而，在高频区，它与K-F系统的情况相同（见[N. Mori和S. Kawashima，Decay property for the Republishenko system with Fourier's type heat conduction，J. Hyperbolic Differential Equations 11（2014）135-157]）或耗散Republishenko系统（参见[K. Ide，K. Haramoto和S. Kawashima，Decay properties of regularity-loss type for dissipative Rishenko system，Math. Models Methods Appl.Sci.18（2008）647-667]），尽管稳定数不同。最后，我们将具有记忆型热效应的K-T系统约化为K-T-Cattaneo系统，研究了K-T系统的衰变性质。
We study the Timoshenko system with Cattaneo’s type heat conduction in the one-dimensional whole space. We investigate the dissipative structure of the system and derive the optimaldecay estimate of the solution in a general situation. Our decay estimate is based on the detailed pointwise estimate of the solution in the Fourier space. We observe that the decay property of our Timoshenko–Cattaneo system is of the regularity-loss type. This decay property is a little different from that of the dissipative Timoshenko system (see [K. Ide, K. Haramoto and S. Kawashima, Decay property of regularity-loss type for dissipative Timoshenko system,Math. Models Methods Appl. Sci.18(2008) 647–667]) in the low frequency region. However, in the high frequency region, it is just the same as that of the Timoshenko–Fourier system (see [N. Mori and S. Kawashima, Decay property for the Timoshenko system with Fourier’s type heat conduction,J. Hyperbolic Differential Equations11(2014) 135–157]) or the dissipative Timoshenko system (see [K. Ide, K. Haramoto and S. Kawashima, Decay property of regularity-loss type for dissipative Timoshenko system,Math. Models Methods Appl. Sci.18(2008) 647–667]), although the stability number is different. Finally, we study the decay property of the Timoshenko system with the thermal effect of memory-type by reducing it to the Timoshenko–Cattaneo system.
DOI：
10.1142/s0218202511500126
发表时间：
2012-02
影响因子：
3.5
作者：
Yongqing Liu;S. Kawashima
通讯作者：
Yongqing Liu;S. Kawashima
影响因子：
3.5
作者：
Takafumi Hosono;S. Kawashima
通讯作者：
Takafumi Hosono;S. Kawashima