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美高梅mgm1888、所2021年系列学术活动(第28场):李景治 教授 南方科技大学

发表于: 2021-05-07   点击: 

报告题目:Determining a random Schrödinger operator: both potential and source are random

报 告 人:李景治 教授 南方科技大学

报告时间:2021年5月15日 9:30

报告地点:美高梅mgm1888三楼天元东北中心第三研讨室

校内联系人:张凯  zhangkaimath@jlu.edu.cn


报告摘要:We present an inverse scattering problem associated with a Schrödinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We then derive two unique recovery results in determining the rough strengths of the random source and the random potential, by using the corresponding far-field data. The first recovery result shows that a single realization of the passive scattering measurements uniquely recovers the rough strength of the random source. The second one shows that, by a single realization of the backscattering data, the rough strength of the random potential can be recovered. The ergodicity is used to establish the single realization recovery. The asymptotic arguments in our study are based on techniques from theory of pseudodifferential operators and microlocal analysis.


报告人简介:李景治,博士,南方科技大学数学系教授,多年来一直从事逆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。