{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:30:16Z","timestamp":1787232616821,"version":"build-2736575974"},"reference-count":16,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"name":"National Key Research and Development Program of China","award":["2024YFA1012300"],"award-info":[{"award-number":["2024YFA1012300"]}]},{"name":"National Key Research and Development Program of China","award":["2023YFA1009100"],"award-info":[{"award-number":["2023YFA1009100"]}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["12071430"],"award-info":[{"award-number":["12071430"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["12525112"],"award-info":[{"award-number":["12525112"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["12371421"],"award-info":[{"award-number":["12371421"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004835","name":"Zhejiang University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004835","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2025,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we study the inverse random source problems for the three-dimensional Helmholtz and Navier equations. The driven source is assumed to be a generalized Gaussian random function whose covariance operator is a classical pseudodifferential operator. We present stability in determining the principal symbol of the covariance operator by using far-field patterns at multiple frequencies in the presence of a potential. The key ingredient in the analysis is employing scattering theory to obtain the analytic domain and an upper bound for the resolvent of the elliptic operator. The analysis only requires data in a finite interval of frequencies.<\/jats:p>","DOI":"10.1137\/24m1720123","type":"journal-article","created":{"date-parts":[[2025,8,20]],"date-time":"2025-08-20T08:00:27Z","timestamp":1755676827000},"page":"1314-1332","source":"Crossref","is-referenced-by-count":1,"title":["Inverse Random Source Problems for the Helmholtz and Navier Equations"],"prefix":"10.1137","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9699-780X","authenticated-orcid":true,"given":"Tianjiao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Hangzhou, 310058 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0626-7609","authenticated-orcid":true,"given":"Xiang","family":"Xu","sequence":"additional","affiliation":[{"name":"1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310058 China 2. Center for Interdisciplinary Applied Mathematics, Zhejiang University, Hangzhou 310058, 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":[[2025,8,20]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1067470"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/16M1088922"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2019.06.006"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/17M1138315"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530519500015"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03537-5"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/200"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-008-0416-6"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2020.1774895"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/21M1467663"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-020-03889-9"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1137\/23M1586331"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2017.01.074"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/20M1334267"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ad99f7"},{"key":"ref16","unstructured":"J. Zhai and Y. Zhao, Increasing Stability Estimates for the Inverse Potential Scattering Problems, arXiv:2306.10211, 2023."}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M1720123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:08:36Z","timestamp":1787231316000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1720123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,20]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,9,30]]}},"alternative-id":["10.1137\/24M1720123"],"URL":"https:\/\/doi.org\/10.1137\/24m1720123","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,20]]}}}