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Determining a random Schrodinger equation with unknown source and potential

发布时间:2019-10-24 作者: 浏览次数:
Speaker: 李景治 DateTime: 2019年10月25日下午3:00-4:00
Brief Introduction to Speaker:

李景治,南方科技大学,教授。

Place: 二楼报告厅
Abstract:This talk studies the direct and inverse scattering problem associated with a time-harmonic random Schr{\"o}dinger 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.