Stability for an inverse source problem of the damped biharmonic plate equation

TL;DR

This paper investigates the stability of an inverse source problem for the damped biharmonic plate equation in three dimensions, highlighting the effects of damping and frequency on stability estimates.

Contribution

It provides new stability estimates using Carleman and decay estimates, revealing how damping and frequency bounds influence inverse problem stability.

Findings

Stability estimate combines Lipschitz data discrepancy and high frequency tail.

High frequency tail decreases as frequency upper bound increases.

Stability depends exponentially on the damping coefficient.

Abstract

This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases. The stability also shows exponential dependence on the constant damping coefficient. The analysis employs Carleman estimates and time decay estimates for the damped plate wave equation to obtain an exact observability bound and depends on the study of the resonance-free region and an upper bound of the resolvent of the biharmonic operator with respect to the complex wavenumber.