雲亭數學講壇2022第22講——王海兵教授

應學院邀請，東南大學王海兵教授将在線作學術報告。

報告題目：A new approach to an inverse source problem for the wave equation

報告摘要：Consider an inverse problem of reconstructing a source term fromboundary 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 theeigenvalues of the Newtonianoperator (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.

報告時間：2022年5月19日下午3:00

報告地點：騰訊會議(會議号:388-379-508)

邀 請 人：孫亮亮副教授

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