Rational decay of a multilayered structure-fluid PDE system
Rational decay of a multilayered structure-fluid PDE system
复制标题
多层结构流体偏微分方程系统的有理衰减
DOI：
10.1016/j.jmaa.2022.126284
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发表时间：
2022
影响因子：
1.3
通讯作者：
Muha, Boris
中科院分区：
文献类型：
--
作者：
Avalos, George;Geredeli, Pelin G.;Muha, Boris
在这项工作中，我们考虑了某多层（厚层）波-（薄层）波-热（流体）相互作用的PDE系统。这种耦合PDE系统已在文献中用于描述哺乳动物血管系统中的血液运输过程。特别地，用二维弹性方程描述了边界界面（薄层）的变形。目前的工作是对下垫流体耗散的稳定作用的程度的调查-跨越边界界面-在厚和薄的结构部件上。（所有三个PDE组件都在各自的几何形状上发展。）在这方面，我们的主要结果是推导出该多层PDE模型经典解的均匀衰减率。为了获得这些估计，这里生成了某些静态多层PDE模型的必要先验不等式，以最终允许应用众所周知的理性衰变的解决准则。
In this work, we consider a certain multilayered (thick layer) wave–(thin layer) wave–heat (fluid) interactive PDE system. Such coupled PDE systems have been used in the literature to describe the blood transport process in mammalian vascular systems. In particular, the deformations of the boundary interface (thin layer) are described via the two dimensional elastic equation. The present work constitutes an investigation of the extent of the stabilizing effects of the underlying fluid dissipation – across the boundary interface – upon both the thick and thin structural components. (All three PDE components evolve on their respective geometries.) In this regard, our main result is the derivation of uniform decay rates for classical solutions of this multilayered PDE model. To obtain these estimates, necessary a priori inequalities for certain static multilayered PDE models are generated here to ultimately allow an application of a wellknown resolvent criterion for rational decay.