This talk studies the direct and inverse scattering problem associated with a time-harmonic random Schrodinger 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.

李景治, 博士, 南方科技大学数学系副教授。2013年入选深圳市海外高层次人才——孔雀人才(B类)。2009年获香港中文大学数学系应用数学哲学博士学位, 获香港数学会最佳博士论文奖; 2009年至2011年, 在苏黎世联邦理工大学数学系做博士后。主要从事计算数学及相关领域, 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。