Wellposedness, spectral analysis and asymptotic stability of a multilayered heat-wave-wave system
Wellposedness, spectral analysis and asymptotic stability of a multilayered heat-wave-wave system
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DOI：
10.1016/j.jde.2020.05.035
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发表时间：
2019-10
期刊：
影响因子：
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通讯作者：
G. Avalos;Pelin G. Geredeli;B. Muha
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文献类型：
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作者：
G. Avalos;Pelin G. Geredeli;B. Muha
在这项工作中，我们考虑了一个多层热浪系统，其中三维热方程与三维波动方程通过二维界面耦合，其动力学由二维波动方程描述。该体系可以看作是某种流固耦合（FSI） PDE模型的简化，其中结构为复合型；也就是说，它由“薄”层和“厚”层组成。我们将系统的适位性与一个强连续半群联系起来，并建立了它的渐近衰减。我们的第一个结果是（FSI） PDE动力学的半群适定性。利用Lumer-Phillips方法，我们证明了流固系统在选定的有限能量数据空间上产生c0半群。作为我们的第二个结果，我们证明了由c0 -半群生成的（FSI）动力学的解对于所有初始数据都渐近地趋于零状态。即（FSI）系统的半群是强稳定的。对于这个稳定性工作，我们分析了发电机A的频谱，并证明了A的频谱不与虚轴相交。
In this work we consider a multilayered heat-wave system where a 3-D heat equation is coupled with a 3-D wave equation via a 2-D interface whose dynamics is described by a 2-D wave equation. This system can be viewed as a simplification of a certain fluid-structure interaction (FSI) PDE model where the structure is of composite-type; namely it consists of a “thin” layer and a “thick” layer. We associate the wellposedness of the system with a strongly continuous semigroup and establish its asymptotic decay. Our first result is semigroup well-posedness for the (FSI) PDE dynamics. Utilizing here a Lumer-Phillips approach, we show that the fluid-structure system generates a C 0-semigroup on a chosen finite energy space of data. As our second result, we prove that the solution to the (FSI) dynamics generated by the C 0-semigroup tends asymptotically to the zero state for all initial data. That is, the semigroup of the (FSI) system is strongly stable. For this stability work, we analyze the spectrum of the generator A and show that the spectrum of A does not intersect the imaginary axis.