An Imaging Inverse Source Problem in a Coupled Diffusion Equations with Uncertain Measurements

Speaker:  Chunlong Sun

Time:      15:00 pm, Jun. 13th

Location: SIST 1D-104

Host:      Wuwei Ren

Abstract:

This talk considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show two Lipschitz-type stability in L² norm and (H¹(.))^* norm, respectively. In practice, we have only a noisy datum of observation and can only observe the measurement data at discrete sensors. Hence, this work further focus on recovering the unknown source from the discrete noisy measurements. We propose a stable inversion scheme and provide probabilistic convergence estimates between the reconstructions and exact solution. We provide several numerical experiments to illustrate and complement our theoretical analysis.

Bio:

Chunlong Sun, Assistant Professor at Nanjing University of Aeronautics and Astronautics. His primary research focuses on theoretical analysis and numerical computation methods for inverse problems in mathematical physics. He has published 20 SCI-indexed papers in journals including Inverse Problems. He has presided over one project each from the National Natural Science Foundation of China Youth Program and the Jiangsu Provincial Natural Science Foundation Youth Program. In 2022, he was selected for the Jiangsu Provincial “Double Innovation Doctor” Talent Program.