Inverse Scattering and Stability Estimates for The Biharmonic Operator

TL;DR

This paper investigates inverse scattering problems for the biharmonic operator, demonstrating unique determination and stability of certain coefficients from high-frequency asymptotics of scattering data.

Contribution

It establishes the unique recovery and stability estimates for curl A and V - 1/2 nabla A using high-frequency scattering asymptotics for the first time.

Findings

High-frequency asymptotics determine curl A and V - 1/2 nabla A uniquely.

Stability estimates for the recovery of these quantities are proved.

Near-field scattering asymptotics also recover the same quantities without additional data.

Abstract

We study an inverse scattering problem of a perturbed biharmonic operator. we show that the high-frequency asymptotic of scattering amplitude of the biharmonic operator uniquely determine the curl A and {V -1/2 nablaA}. We also study the near-field scattering problem and show that the high-frequency asymptotic expansion up to a certain error in terms of frequency lambda recovers the same two above quantities with no additional information about A and V. We also prove stability estimates for curl A and {V -1/2 nablaA}.