On an inverse problem for the plate equation with passive measurement

TL;DR

This paper investigates an inverse problem for the plate equation, demonstrating unique recovery of unknown density and sources from passive boundary data using asymptotic and harmonic analysis techniques.

Contribution

It introduces novel methods for simultaneously identifying density and sources in the plate equation from passive measurements, advancing inverse problem theory.

Findings

Unique identifiability of density and sources

Use of asymptotic analysis for inverse problems

Application of harmonic analysis on integral transforms

Abstract

This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density and internal sources from passive boundary measurement. The proof mainly relies on the asymptotic analysis and harmonic analysis on integral transforms