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.
包刚多次应邀在重要国际会议作大会报告，论文发表在包括国际顶尖刊物J. Ameri.Math. Soc.等学术期刊达150余篇。现任Inverse Problems, SIAM J. Appl. Math., SIAM J. Numer. Anal., J. Differential Equations等十余个国际知名期刊编委。2003年，包刚获得冯康科学计算奖。2016年，包刚当选为美国工业与应用数学会会士（SIAM Fellow）。