Simultaneous Reconstruction of Multiple Unknowns in Stokes-Darcy System from Partial Boundary Data

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 $\mu$, the interface $\Gamma$, 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.