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甬江数学讲坛讲276讲(2022年第60讲)
2022-09-19 16:21     (点击:)

报告题目:A new approach to an inverse source problem for the wave equation

人:王海兵(东南大学 教授)

会议时间:2022/9/22 下午2:00开始

会议地点:腾讯会议,会议号:506-106-043

报告摘要: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.

报告人简介:王海兵,东南大学数学学院教授,博士研究生导师,主要从事数学物理反问题的研究。2012年获得北海道大学和东南大学的理学博士学位。现任中国数学会计算数学分会常务理事。目前正主持一项国家自然科学基金面上项目,已发表论文三十余篇,代表性研究成果发表于SIAM系列,IP, JDE, JCP等学术刊物。

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