Lipschitz Stability for an Inverse Problem of Biharmonic Wave Equations with Damping

Abstract

We study the recovery of density and initial displacement for a clamped biharmonic wave equation with known damping. For prescribed smooth finite-dimensional coefficient and initial-state profiles, we prove strong differentiability of the boundary observation map and establish local Lipschitz stability under an injective sensitivity condition. The proof combines natural-energy estimates with higher-regularity bounds in the generator graph norm. For a homogeneous density and a known nonzero initial mode with unknown amplitude, we prove injectivity and a global Lipschitz estimate on compact parameter rectangles, using a single curvature trace. The constants are uniform on fixed bounded damping intervals under the stated conditions. Independent repeated-noise experiments are reported for the proved one-mode class and for an additional finite-bandwidth square-plate configuration, with refinement checks and reproducibility files.

arXiv comment17 pages