论文标题
有界的半群良好的良好性，以与材料导数的线性压缩流量结构PDE相互作用
Bounded Semigroup Wellposedness for a Linearized Compressible Flow Structure PDE Interaction with Material Derivative
论文作者
论文摘要
我们考虑了可压缩的流量结构相互作用（FSI）PDE系统，该系统涉及某些参考休息状态。可变形的界面是在基础和无界材料衍生术语产生的环境场的效果下，这进一步有助于FSI系统的非分离性，相对于标准能量内部产品。在这项工作中，我们表明，在适当的子空间上，只有一个维度小于整个有限能量空间，FSI系统已得到充分量，并且与连续的半群相关，该连续半群是\ emph {均匀界限}的时间。我们的方法涉及建立相对于特殊的内部产物建立最大的消散性，该产品与给定有限能量空间相当于标准内部产品。除其他技术功能外，必要的PDE估计需要调用给定可压缩FSI系统固有的乘数。
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 non-dissipativity 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 \emph{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 necesssary PDE estimates require the invocation of a multiplier which is intrinsic to the given compressible FSI system.
