Direct and inverse problems for the Schrödinger operator in a three-dimensional planar waveguide

Abstract

In this paper, we study the meromorphic continuation of the resolvent for the Schrödinger operator in a three-dimensional planar waveguide. We prove the existence of a resonance-free region and an upper bound for the resolvent. As an application, the direct source problem is shown to have a unique solution under some appropriate assumptions. Moreover, an increasing stability is achieved for the inverse source problem of the Schrödinger operator in the waveguide by using limited aperture Dirichlet data only at multiple frequencies. 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.

arXiv commentarXiv admin note: text overlap with arXiv:2102.04631

References in corpus (4)

• The $L^p$ boundedness of wave operators for Schrödinger Operators with threshold singularities
• On increasing stability in the two dimensional inverse source scattering problem with many frequencies
• A direct approach to imaging in a waveguide with perturbed geometry
• Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions