论文标题
多层结构流体PDE系统的合理衰变
Rational Decay of A Multilayered Structure-Fluid PDE System
论文作者
论文摘要
在这项工作中，我们考虑了一定的多层（厚层）波 - （薄层）波 - 热（流体）交互式PDE系统。这种耦合的PDE系统已在文献中用于描述哺乳动物血管系统中的血液传输过程。特别是，通过二维弹性方程来描述边界界面（薄层）的变形。目前的工作构成了对厚度和薄的结构成分均对基础流体耗散（跨边界界面）稳定作用的程度的研究。 （所有三个PDE组件都在其各自的几何形状上演变。）在这方面，我们的主要结果是该多层PDE模型的经典溶液的均匀衰减速率的推导。为了获得这些估计，在这里生成了必要的某些静态多层PDE模型的先验不平等，以最终允许应用众所周知的分解标准进行合理衰变。
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.
