報(bào)告承辦單位: 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院

報(bào)告內(nèi)容: Inverse Source Problems for Wave Propagation

報(bào)告人姓名: 李培軍

報(bào)告人所在單位: 美國普渡大學(xué)數(shù)學(xué)系

報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜: 教授

報(bào)告時(shí)間: 2019年5月25日周六下午4:30－5:30

報(bào)告地點(diǎn): 云塘校區(qū)理科樓A-419

報(bào)告人簡介: 李培軍,2005博士畢業(yè)于美國密西根州立大學(xué),現(xiàn)任普渡大學(xué)數(shù)學(xué)系教授。主要從事科學(xué)計(jì)算、數(shù)值分析和偏微分方程反問題等的工作,特別是光學(xué)、電磁學(xué)和波動(dòng)方程中正反散射問題的研究。先后承擔(dān)和主持了5項(xiàng)美國國家自然科學(xué)基金項(xiàng)目,發(fā)表論文80余篇。曾獲美國國家自然科學(xué)基金杰出獎(jiǎng)項(xiàng)(NSF Career Award)及 2015 年度Calderon Prize。

報(bào)告摘要：The inverse source problems, as an important research subject in inverse scattering theory, have significant applications in diverse scientific and industrial areas such as antenna design and synthesis, medical imaging, and optical tomography. Although they have been extensively studied, some of the fundamental questions, such as uniqueness, stability, and uncertainty quantification, still remain to be answered. In this talk, our recent progress will be discussed on the inverse source problems for acoustic, elastic, and electromagnetic waves. I will present a new approach to solve the stochastic inverse source problems. The stability will be addressed for the deterministic counterparts of the inverse source problems. We show that the increasing stability can be achieved by using the Dirichlet boundary data at multiple frequencies.