多层结构-流体PDE系统的有理衰减
Rational Decay of A Multilayered Structure-Fluid PDE System
摘要：
本文考虑了一类多层（厚层）波-（薄层）波-热（流体）相互作用的偏微分方程系统。这种偶联的PDE系统已在文献中用于描述哺乳动物血管系统中的血液转运过程。特别地，边界界面（薄层）的变形通过二维弹性方程来描述。目前的工作构成了一个调查的程度上的稳定效果的基础流体耗散-跨越边界界面-厚和薄的结构组件。(All三个PDE分量在它们各自的几何形状上演变。在这方面，我们的主要结果是推导出这个多层PDE模型的经典解的均匀衰减率。为了获得这些估计，必要的先验不等式，某些静态多层PDE模型在这里产生的，最终允许一个著名的预解式标准的合理衰减的应用程序。
英文摘要：
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.
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