Article Contents
Article Contents

# Inverse scattering and stability for the biharmonic operator

The author is partially supported by a NSF DMS grants No. 1600327 and 1900475
• We investigate the inverse scattering problem of the perturbed biharmonic operator by studying the recovery process of the magnetic field ${\mathbf{A}}$ and the potential field $V$. We show that the high-frequency asymptotic of the scattering amplitude of the biharmonic operator uniquely determines ${\rm{curl}}\ {\mathbf{A}}$ and $V-\frac{1}{2}\nabla\cdot{\mathbf{A}}$. We study the near-field scattering problem and show that the high-frequency asymptotic expansion up to an error $\mathcal{O}(\lambda^{-4})$ recovers above two quantities with no additional information about ${\mathbf{A}}$ and $V$. We also establish stability estimates for ${\rm{curl}}\ {\mathbf{A}}$ and $V-\frac{1}{2}\nabla\cdot{\mathbf{A}}$.

Mathematics Subject Classification: 35R30, 47A40, 31B30.

 Citation:

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