SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1711-1744, January 2021.
We consider a compressible flow-structure interaction (FSI) PDE system which is linearized about some reference rest state. The deformable interface is under the effect of an ambient field generated by the underlying and unbounded material derivative term which further contributes to the nondissipativity of the FSI system with respect to the standard energy inner product. In this work we show that, on an appropriate subspace, only one dimension less than the entire finite energy space, the FSI system is wellposed and is moreover associated with a continuous semigroup which is uniformly bounded in time. Our approach involves establishing maximal dissipativity with respect to a special inner product which is equivalent to the standard inner product for the given finite energy space. Among other technical features, the necessary PDE estimates require the invocation of a multiplier which is intrinsic to the given compressible FSI system.

中文翻译：

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线性可压缩流结构PDE与材料导数相互作用的有界半群适定性

SIAM数学分析杂志，第53卷，第2期，第1711-1744页，2021年1月。
我们考虑了一个可压缩的流-结构相互作用（FSI）PDE系统，该系统关于某些参考静止状态线性化。可变形界面在由基础的和无界的材料导数项生成的环境场的作用下，这进一步有助于FSI系统相对于标准能量内积的非耗散性。在这项工作中，我们表明，在一个适当的子空间上，仅比整个有限能量空间小一维的FSI系统处于良好的位置，而且与时间上有界的连续半群相关。我们的方法涉及针对特定内部乘积建立最大耗散性，该特定内部乘积等效于给定有限能量空间的标准内部乘积。除其他技术功能外，