The asymptotic behavior of the linear transmission problem in viscoelasticity
The asymptotic behavior of the linear transmission problem in viscoelasticity
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DOI：
10.1002/mana.201200319
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发表时间：
2014-04
影响因子：
1
通讯作者：
M. Alves;J. Rivera;M. Sepúlveda;O. V. Villagrán;M. Z. Garay
中科院分区：
文献类型：
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作者：
M. Alves;J. Rivera;M. Sepúlveda;O. V. Villagrán;M. Z. Garay
我们考虑了一个局部Kelvin‐Voigt粘弹性阻尼的传输问题。我们的主要结果是表明相应的半群（SA(t)）t≥0不是指数稳定的，而是当初始数据取到D(A)域时，系统的解多项式地衰减到零为1/t2。此外，我们还证明了这种衰减速率是最优的。最后，我们使用二阶格式（Newmark - β方法）来保证能量的衰减，给出了一些数值例子来证明这种多项式渐近行为。
We consider a transmission problem with localized Kelvin‐Voigt viscoelastic damping. Our main result is to show that the corresponding semigroup (SA(t))t≥0 is not exponentially stable, but the solution of the system decays polynomially to zero as 1/t2 when the initial data are taken over the domain D(A). Moreover, we prove that this rate of decay is optimal. Finally, using a second order scheme that ensures the decay of energy (Newmark‐β method), we give some numerical examples which demonstrate this polynomial asymptotic behavior.