Increasing Stability of Determining Both the Potential and Source for the Biharmonic Wave Equation

Abstract

This paper is concerned with the inverse scattering problems of simultaneously determining the unknown potential and unknown source for the biharmonic wave equation. We first derive an increasing stability estimate for the inverse potential scattering problem without a priori knowledge of the source function by multi-frequency active boundary measurements. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the potential function, where the latter decreases as the upper bound of the frequency increases. The key ingredients in the analysis are employing scattering theory to derive an analytic domain and resolvent estimates and an application of the quantitative analytic continuation principle. Utilizing the derived stability for the inverse potential scattering, we further prove an increasing stability estimate for the inverse source problem. The main novelty of this paper is that both the source and potential functions are unknown.