荔园数学讲坛: Determining a random Schrödinger equation with unknown source and potential

主讲人：南方科技大学 李景治教授

时间：2022年03月31日15:00–16:00

腾讯会议号：739-595-493

会议链接：https://meeting.tencent.com/dm/58oApAIfWT07

内容摘要： 

This talk studies the direct and inverse scattering problem associated with a time-harmonic random Schrödinger equation with a Gaussian white noise source term. We establish the well-posedness of the direct scattering problem and obtain three uniqueness results in determining the variance of the source term, the potential and the mean of the source term, sequentially, by the corresponding far-field measurements. The first one shows that a single realization of the passive scattering measurement can uniquely recover the variance of the source term, without knowing the other two unknowns. The second shows that if active scattering measurement is further used, then a single realization can uniquely recover the potential function without knowing the source term. The last one shows that if full measurements are used, then both the potential and the random source can be uniquely recovered.

主讲人简介: 

李景治，南方科技大学数学系教授。多年来一直从事反问题相关偏微分方程数值解法的研究，在计算数学的理论研究和数值模拟方面取得了一系列的研究成果。目前主要研究领域涉及到反问题理论与计算方法，形状优化与微分形式统一理论，科学计算，有限元方法。特别是发展了微分形式下的Stein延拓定理，并在数学物理反问题中的反演成像理论与算法方面做出重要贡献。近年来，在国内外有影响的学术刊物（包括CMP、IP、SIAM系列、JFA、JDE、Numer Math、JCP等）上发表了80多篇，均为SCI收录，主持国家自然科学基金3项，深圳市杰青项目，参与国自然重点项目一项。