報告題目：A new approach to an inverse source problem for the wave equation
報 告 人：王海兵 教授 東南大學
報告時間：2022年5月30日 9:00-10:00
報告地點：騰訊會議ID：505-778-875， 密碼：220530
或點擊鍊接直接加入會議：https://meeting.tencent.com/dm/jfaN0uR7Gugg
校内聯系人：張德悅 dyzhang@jlu.edu.cn
報告摘要：Consider an inverse problem of reconstructing a source term from boundary measurements for the wave equation. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small particles, enjoying a high contrast, into the medium. For this purpose, we first derive the asymptotic expansion of the wave field, based on the time-domain Lippmann-Schwinger equation. The dominant term in the asymptotic expansion is expressed as an infinite series in terms of the eigenvalues of the Newtonian operator (for the pure Laplacian). Such expansions are useful under a certain scale between the size of the particles and their contrast. Second, we observe that the relevant eigenvalues appearing in the expansion have non-zero averaged eigenfunctions. By introducing a Riesz basis, we reconstruct the wave field, generated before injecting the particles, on the center of the particles. Finally, from these (internal values of these) last fields, we reconstruct the source term (by numerical differentiation for instance). A significant advantage of our approach is that we only need the measurements for a single point away from the support of the source.
報告人簡介：王海兵，東南大學伟德线上平台教授，博士研究生導師，主要從事數學物理反問題的研究。2012年獲得北海道大學和東南大學的理學博士學位。現任中國數學會計算數學分會常務理事。目前正主持一項國家自然科學基金面上項目，已發表論文三十餘篇，代表性研究成果發表于SIAM系列，IP, JDE, JCP等學術刊物。
