【Academic Seminar】Determining a random Schroedinger equation with unknown source and potential
Topic: Determining a random Schroedinger equation with unknown source and potential
Speaker: Prof. Jingzhi LI, Southern University of Science and Technology
Time & Date: 10:30am-11:30am, September 23, 2020
Venue: Zoom, Meeting ID: 559 916 3678
This talk studies the direct and inverse scattering problem associated with a time-harmonic random Schroedinger 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.
Jingzhi Li has been a Professor of Mathematics at SUSTech since 2020. Prior to that, he was an assistant and associate professor at CAS and SUSTech, respectively, from 2012 to 2019. Prof. Jingzhi Li’s research focuses on computational mathematics, applied probability and inverse problems. He received his Ph.D. from the Chinese University of Hong Kong and was a postdoctoral fellow at ETH Zurich from 2009 to 2011.