On the Stability of Damped Timoshenko Systems: Cattaneo Versus Fourier Law
On the Stability of Damped Timoshenko Systems: Cattaneo Versus Fourier Law
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DOI：
10.1007/s00205-009-0220-2
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发表时间：
2009-02
影响因子：
2.5
通讯作者：
Hugo D. Fernández Sare;R. Racke
中科院分区：
文献类型：
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作者：
Hugo D. Fernández Sare;R. Racke
我们考虑耦合到热方程的双曲型振动系统，该热方程通过热传导来模拟耗散效应。虽然傅立叶热传导定律下的指数稳定性成立，但事实证明，通过卡塔内奥定律的耦合不会产生指数稳定的系统。这似乎是第一个例子，通过改变卡塔内奥定律消除傅立叶定律中固有的无限传播速度的悖论，导致指数稳定性的损失。实际上，对于具有历史的系统，傅立叶定律保持了不具有热传导的纯Alkoshenko系统的指数稳定性，但引入Cattaneo耦合甚至破坏了这一性质。
We consider hyperbolic Timoshenko-type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. While exponential stability under the Fourier law of heat conduction holds, it turns out that the coupling via the Cattaneo law does not yield an exponentially stable system. This seems to be the first example that a removal of the paradox of infinite propagation speed inherent in Fourier’s law by changing to the Cattaneo law causes a loss of the exponential stability property. Actually, for systems with history, the Fourier law keeps the exponential stability known for the pure Timoshenko system without heat conduction, but introducing the Cattaneo coupling even destroys this property.