{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T12:51:05Z","timestamp":1787748665988,"version":"build-2784847793"},"reference-count":16,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["12425112"],"award-info":[{"award-number":["12425112"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["12071236"],"award-info":[{"award-number":["12071236"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"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\/501100004835","name":"Zhejiang University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004835","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"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2025,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we investigate well-posedness of time-harmonic scattering of elastic waves by unbounded rigid rough surfaces in three dimensions. Both deterministic and random surfaces are investigated through the variational approach. In a deterministic setting, the rough surface is assumed to be a Lipschitz profile, which lies within a finite distance of a flat plane. The elastic scattering is caused by a source term with a compact support above the rough surface. A stability estimate is derived at an arbitrary frequency, with explicit dependance of the bound on the excitation frequency and geometry of rough surfaces. Based on the a priori dependence on the frequency together with the measurability and P-essentially separability of the randomness, we obtain a similar bound for the time-harmonic elastic scattering by random surfaces.<\/jats:p>","DOI":"10.1137\/24m1640306","type":"journal-article","created":{"date-parts":[[2025,4,23]],"date-time":"2025-04-23T08:58:11Z","timestamp":1745398691000},"page":"1964-1989","source":"Crossref","is-referenced-by-count":1,"title":["Time-Harmonic Elastic Scattering by Unbounded Deterministic and Random Rough Surfaces in Three Dimensions"],"prefix":"10.1137","volume":"57","author":[{"given":"Guanghui","family":"Hu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianjiao","family":"Wang","sequence":"additional","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":"School of Mathematical Sciences, 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":[[2025,4,21]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S030500410003629X"},{"key":"ref2","volume-title":"Wave Propagation in Elastic Solids","author":"Achenbach J. 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Kupradze, et\u00a0al., Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North-Holland, Amsterdam, 1979."},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/18M119327X"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.4208\/csiam-am.SO-2023-0001"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M1640306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:20:12Z","timestamp":1787322012000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1640306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,21]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,4,30]]}},"alternative-id":["10.1137\/24M1640306"],"URL":"https:\/\/doi.org\/10.1137\/24m1640306","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,21]]}}}