報告題目：Determining a random Schrödinger operator: both potential and source are random
報 告 人：李景治 教授 南方科技大學
報告時間：2021年5月15日 9:30
報告地點：伟德线上平台三樓天元東北中心第三研讨室
校内聯系人：張凱 zhangkaimath@jlu.edu.cn
報告摘要：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.
報告人簡介：李景治，博士，南方科技大學數學系教授，多年來一直從事逆問題相關偏微分方程數值解法的研究，在計算數學的理論研究和數值模拟方面取得了一系列的研究成果。目前主要研究領域涉及到反問題理論與計算方法，形狀優化與微分形式統一理論，科學計算，有限元方法。特别是發展了微分形式下的Stein延拓定理，并在數學物理反問題中的反演成像理論與算法方面做出重要貢獻。
