Lack of exponential stability to Timoshenko system with viscoelastic Kelvin–Voigt type

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• 作者：Andréia Malacarne…
• 刊名：Zeitschrift f¨¹r angewandte Mathematik und Physik
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：67
• 期：3
• 全文大小：490 KB
• 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
• 出版者：Springer Basel
• ISSN：1420-9039
• 卷排序：67

文摘

We study the Timoshenko systems with a viscoelastic dissipative mechanism of Kelvin–Voigt type. We prove that the model is analytical if and only if the viscoelastic damping is present in both the shear stress and the bending moment. Otherwise, the corresponding semigroup is not exponentially stable no matter the choice of the coefficients. This result is different to all others related to Timoshenko model with partial dissipation, which establish that the system is exponentially stable if and only if the wave speeds are equal. Finally, we show that the solution decays polynomially to zero as \({t^{-1/2}}\) , no matter where the viscoelastic mechanism is effective and that the rate is optimal whenever the initial data are taken on the domain of the infinitesimal operator.KeywordsTimoshenko systemKelvin–VoigtAnalyticityLack of exponential stabilityPolynomial stabilityOptimal decay rate