基于部分边界数据的Stokes-Darcy系统中多个未知量的同时重建
Simultaneous Reconstruction of Multiple Unknowns in Stokes-Darcy System from Partial Boundary Data
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中文总结 AI 辅助
针对流体-多孔介质耦合的Stokes-Darcy系统，提出一种基于内部传输问题构造的新方法，从局部边界柯西数据同时恢复粘度系数、界面和内部物体，并证明全局唯一性。
中文摘要 AI 辅助
本文研究了一个耦合Stokes-Darcy系统的逆边值问题，该系统模拟流体-多孔介质相互作用，其中自由流动区域中嵌入了一个未知的固体物体。我们从局部边界柯西数据同时恢复粘度系数$\mu$、界面$\Gamma$和内部物体$D$。引入了一种基于内部传输问题构造的新方法，该方法可以放大解的奇异性。我们建立了一个全局唯一性定理，表明所有三个未知量都由边界测量唯一确定。
英文摘要
This paper studies an inverse boundary value problem for a coupled Stokes-Darcy system modeling fluid-porous medium interaction, with an unknown solid object embedded in the free-flow region. We simultaneously recover the viscosity coefficient $μ$, the interface $Γ$, and the internal object $D$ from localized boundary Cauchy data. A novel method based on the construction of an interior transmission problem is introduced, which can amplify the singularity of solutions. We establish a global uniqueness theorem, showing that all three unknowns are uniquely determined by the boundary measurements.
