ABSTRACT

In this work we analyze the porous elastic system with a viscoelastic dissipative mechanism of Kelvin–Voigt type. We prove that the semigroup associated with the model is analytic if and only if the viscoelastic damping is present in both equations of the system. Otherwise, there exist lack of exponential stability, independently of any relationship between the coefficients. This result is different to all others related to porous-elastic model with partial dissipation. In this case we prove that the semigroup decays as $t^{-1/2}$. Moreover we show that the rate is optimal.

中文翻译：

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具有 Kelvin-Voigt 的多孔弹性系统：分析性和最佳衰减率

摘要

在这项工作中，我们分析了具有 Kelvin-Voigt 型粘弹性耗散机制的多孔弹性系统。我们证明了与模型相关的半群是解析的当且仅当系统的两个方程中都存在粘弹性阻尼。否则，存在指数稳定性的缺乏，与系数之间的任何关系无关。该结果与所有其他与具有部分耗散的多孔弹性模型相关的结果不同。在这种情况下，我们证明半群衰减为${吨}^{-1/2}$. 此外，我们表明该速率是最优的。