A new approach to an inverse source problem for the wave equation

发布时间：2023-06-14 作者：浏览次数：

Speaker:	王海兵教授	DateTime:	2023年6月15日（周四） 16：00–17:30
Brief Introduction to Speaker: 王海兵东南大学教授		Place:	腾讯会议 ID: 803 137 417
Abstract: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 last fields, we reconstruct the source term. A signif...