Abstract

Inverse scattering problems arise in diverse application areas, such as geophysical prospecting, near-field and nano optical imaging, and medical imaging. For a given wave incident on a medium enclosed by a bounded domain, the scattering (direct) problem is to determine the scattered field or the energy distribution for the known scatterer. The inverse problem is to determine the scatterer from the boundary measurements of the fields. Although significant recent progress has been made for solving the inverse problem, many challenging mathematical and computational issues remain unresolved. In particular, the severe ill-posedness has thus far limited in many ways the scope of inverse problem methods in practical applications. In this talk, the speaker will first introduce several inverse scattering problems of broad interest and discuss recent developments in the mathematical and computational studies of the problems. Based on multi-frequency data, effective computational and mathematical approaches will be presented for overcoming the ill-posedness of the inverse problems. Selected mathematical and computational results will be highlighted. In addition, recent stability results for inverse scattering problems in elasticity will also be presented. The talk will be concluded by remarks on related topics and open problems.

Bio

Gang Bao, Chair Professor and Dean of the School of Mathematical Sciences at Zhejiang University.  After his PhD degree at Rice University in 1991, he was a Research Associate at Rice University and the IMA, University of Minnesota (1991-1994), Assistant and Tenured Associate Professor at University of Florida (1994-1999), and Full Professor at Michigan State University (1999-2014). He was the Founding Director of the Michigan Centre for Industrial and Applied Mathematics at Michigan State University (2006-2014). He joinned Zhejiang University in 2010. A recipient of the Feng Kang Prize on Scientific Computing in 2003 and the MSU University Distinguished Faculty Awardin 2007, and elected SIAM Fellow in 2016, Dr. Bao’s research interests include inverse problems for partial differential equations; mathematics and computation of diffractive optics, nonlinear optics, nano-optics, and electromagnetics. He has published over 150 papers in leading research journals including J. Ameri. Math.Soc.,Arch. Rational Mech. Anal., J. Math.Pures Appl.,Trans of AMS, Math. Comp., as well as Nature Nanotechnology. Dr. Bao is currently on the editorial boards of over 10 International research journals on mathematics including SIAM J. Appl. Math, SIAM J. Numer. Anal.,  J. Differential Equations, Inverse Problems, Inverse Problems and Imaging, and DCDS B.