Rational rates of uniform decay for strong solutions to a fluid-structure PDE system
Rational rates of uniform decay for strong solutions to a fluid-structure PDE system
复制标题
流固偏微分方程系统强解的合理均匀衰减率
DOI：
10.1016/j.jde.2015.01.037
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发表时间：
2015
影响因子：
2.4
通讯作者：
F. Bucci
中科院分区：
文献类型：
--
作者：
G. Avalos;F. Bucci
在这项工作中，我们研究了一个完善的流固耦合偏微分方程 (PDE) 模型解的一致稳定性特性。所考虑的偏微分方程系统包括在三维空腔内演化的斯托克斯流；此外，还调用基尔霍夫板方程来描述沿腔壁（固定）部分（例如 Ω）的位移。相应流体和结构动力学之间的接触发生在边界界面 Ω 上。论文的主要结果如下：复合偏微分方程组的解，对应于平滑的初始数据，以O(1/t)的速率衰减。我们的证明方法取决于对 C 0 半群多项式衰变的相对较新的求解准则的适当调用。虽然所述准则提供的表征源于算子理论和泛函分析的背景，但这里所需的工作完全属于偏微分方程的领域。
In this work we investigate the uniform stability properties of solutions to a well-established partial differential equation (PDE) model for a fluid-structure interaction. The PDE system under consideration comprises a Stokes flow which evolves within a three-dimensional cavity; moreover, a Kirchhoff plate equation is invoked to describe the displacements along a (fixed) portion–say, Ω–of the cavity wall. Contact between the respective fluid and structure dynamics occurs on the boundary interface Ω. The main result in the paper is as follows: the solutions to the composite PDE system, corresponding to smooth initial data, decay at the rate of O (1/t). Our method of proof hinges upon the appropriate invocation of a relatively recent resolvent criterion for polynomial decays of C 0-semigroups. While the characterization provided by said criterion originates in the context of operator theory and functional analysis, the work entailed here is wholly within the realm of PDE.