组织者 Organizer：李宏杰

报告摘要：

This talk concerns the direct and inverse scattering of the Schrödinger equation in a three-dimensional planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the Schrödinger operator in such a geometry. Then several inverse problems are investigated. First, given the potential function, we prove the uniqueness of the inverse source problem with multi-frequency data. We also develop a Fourier-based method to reconstruct the source function. The capability of this method will be numerically illustrated by examples. Second, the uniqueness and increased stability of an inverse potential problem from data generated by incident waves are achieved. Third, we prove the uniqueness of simultaneously determining the source and potential by active boundary data generated by incident waves.