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MS56 2: Inverse Problems of Transport Equations and Related Topics
Time:
Monday, 04/Sept/2023:
4:00pm - 6:00pm
Session Chair: Ru-Yu Lai Session Chair: Hanming Zhou
Location:VG2.106
Presentations
Reconstruction of the doping profile in Vlasov-Poisson
Weiran Sun1, Ru-yu Lai2, Qin Li3
1Simon Fraser University, Canada; 2University of Minnesota, USA; 3University of Wisconsin Madison, USA
In this talk we show how the singular decomposition method can be applied to recover the doping profile in the Vlasov-Poisson equation.
Quantitative reconstructions in inverse transport problems
Kui Ren
Columbia University, United States of America
In many practical applications of inverse problems, the data measured contain unknown normalization constants due to the unknown strength of the illumination sources. In such cases, it is usually impossible to quantitatively reconstruct the coefficients of interest. We show, mainly computationally, that one can actually have quantitative reconstructions for some inverse transport problems where redundancy in data helps us to eliminate the unknown normalization constant encoded in the illumination sources.
Imaging with two-photon absorption optics
Yimin Zhong
Auburn University, United States of America
In this talk, we briefly talk about the inverse boundary/medium problems with the semilinear transport model which has a natural application in two-photon absorption optics. For the inverse boundary problem, we adopted the usual linearization technique and prove the uniqueness of reconstruction. For the inverse medium problems, we consider the problem from photoacoustic imaging specifically in static and time-dependent settings and prove the uniqueness of the reconstruction for the absorption coefficients.
