{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T22:12:33Z","timestamp":1788473553635,"version":"build-2803163510"},"reference-count":31,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971133"],"award-info":[{"award-number":["11971133"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371421"],"award-info":[{"award-number":["12371421"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2024,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multifrequency phaseless data. In the first stage, we introduce some artificial auxiliary point sources to the inverse source system and establish a phase retrieval formula. Theoretically, we point out that the phase can be uniquely determined and estimate the stability of this phase retrieval approach. Once the phase information is retrieved, the Fourier method is adopted to reconstruct the source function from the phased multifrequency data. The proposed method is easy to implement and there is no forward solver involved in the reconstruction. Numerical experiments are conducted to verify the performance of the proposed method.<\/jats:p>","DOI":"10.1137\/24m162889x","type":"journal-article","created":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T04:01:46Z","timestamp":1725336106000},"page":"A2799-A2818","source":"Crossref","is-referenced-by-count":8,"title":["Inverse Source Problem of the Biharmonic Equation from Multifrequency Phaseless Data"],"prefix":"10.1137","volume":"46","author":[{"given":"Yan","family":"Chang","sequence":"first","affiliation":[{"name":"School of Mathematics, Harbin Institute of Technology, Harbin, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4477-7666","authenticated-orcid":true,"given":"Yukun","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mathematics, Harbin Institute of Technology, Harbin, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Zhao","sequence":"additional","affiliation":[{"name":"Corresponding author. School of Mathematics and Statistics, and Key Lab NAA\u2013MOE, Central China Normal University, Wuhan 430079, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,9,3]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aaf097"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/25\/5\/055005"},{"key":"ref3","volume-title":"Mathematical Methods for Physicists","author":"Arfken G.","year":"2013"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/548\/10835"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/140993648"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1002\/hbm.25586"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/19M1295660"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2399924"},{"key":"ref9","doi-asserted-by":"crossref","unstructured":"Y. Chang, Y. Guo, T. Yin, and Y. 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