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

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.