Direct and inverse scattering problems for the Schrödinger equation in a 3D planar waveguide

Yukun Guo 郭玉坤

哈尔滨工业大学

郭玉坤，哈尔滨工业大学数学学院教授、博士生导师。本科和博士均毕业于吉林大学计算数学专业。研究领域为数学物理反问题，主要方向为波动方程反散射问题的理论分析与数值计算。在 SIAM系列、Inverse Problems、Journal of Computational Physics等期刊发表学术论文四十余篇。主持和参与多项与反问题相关的国家自然科学基金项目。

# Organizer

李宏杰

# Time

Friday, 9:30-10:30

Dec. 26, 2025

# Venue

C654, Shuangqing Complex Building

#Abstract

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.