论文标题
具有局部开尔文 - voigt阻尼的弹性 - 维易弹弹性波的稳定性结果，内部或边界时间延迟
Stability results for an elastic-viscoelastic waves interaction systems with localized Kelvin-Voigt damping and with an internal or boundary time delay
论文作者
论文摘要
我们研究了一维波方程的稳定性，并具有非平滑的局部内部粘弹性阻尼，开尔文 - voigt类型以及边界或局部内部延迟反馈。本文的主要新颖性是开尔文 - voigt和延迟阻尼都是通过非平滑系数定位的。如果开尔文 - voigt阻尼与尖端远处局部局部，并且波浪受到局部分布的内部或边界延迟反馈，我们证明系统的能量在T^{-4}类型的多种一级衰减。但是，只要开尔文 - voigt阻尼位于边界的一部分附近，并且时间延迟阻尼作用在第二个边界上，则建立了系统能量的指数衰减。而当kelvin-voigt和内部延迟阻尼都通过尖端附近的非平滑系数定位时，系统的能量在T^{ - 4}型的多个衰减。频域参数与分段乘数技术相结合。
We investigate the stability of a one-dimensional wave equation with non smooth localized internal viscoelastic damping of Kelvin-Voigt type and with boundary or localized internal delay feedback. The main novelty in this paper is that the Kelvin-Voigt and the delay damping are both localized via non smooth coefficients. In the case that the Kelvin-Voigt damping is localized faraway from the tip and the wave is subjected to a locally distributed internal or boundary delay feedback, we prove that the energy of the system decays polynomially of type t^{-4}. However, an exponential decay of the energy of the system is established provided that the Kelvin-Voigt damping is localized near a part of the boundary and a time delay damping acts on the second boundary. While, when the Kelvin-Voigt and the internal delay damping are both localized via non smooth coefficients near the tip, the energy of the system decays polynomially of type t^{-4}. Frequency domain arguments combined with piecewise multiplier techniques are employed.
