{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T18:14:58Z","timestamp":1789582498828,"version":"build-2803163510"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"name":"National Key Research and Development Program of China","award":["2023YFB3002400"],"award-info":[{"award-number":["2023YFB3002400"]}]},{"name":"Fundamental Research Funds for the Central Universities, Sun Yat-sen University","award":["24qnpy304"],"award-info":[{"award-number":["24qnpy304"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101627"],"award-info":[{"award-number":["12101627"]}],"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":["12371423"],"award-info":[{"award-number":["12371423"]}],"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":["12241104"],"award-info":[{"award-number":["12241104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2025,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this work the authors consider the recovery of the point source in the heat equation. The used data are the sparse boundary measurements. The uniqueness theorem of the inverse problem is given. After that, the numerical reconstruction is considered. We propose a numerical method to reconstruct the location of a Dirac point source by reformulating the inverse problem as a least-squares optimization problem, which is efficiently solved using a gradient descent algorithm. Numerical experiments confirm the accuracy of the proposed method and demonstrate its robustness to noise.<\/jats:p>","DOI":"10.1137\/25m1725620","type":"journal-article","created":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T07:24:37Z","timestamp":1760081077000},"page":"2337-2354","source":"Crossref","is-referenced-by-count":1,"title":["Determine the Point Source of the Heat Equation with Sparse Boundary Measurements"],"prefix":"10.1137","volume":"85","author":[{"given":"Qiling","family":"Gu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Southern University of Science and Technology (SUSTech), 1088 Xueyuan Boulevard, University Town of Shenzhen, Xili, Nanshan, Shenzhen, Guangdong Province, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8368-3465","authenticated-orcid":true,"given":"Wenlong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Corresponding author. Department of Mathematics, Southern University of Science and Technology (SUSTech), 1088 Xueyuan Boulevard, University Town of Shenzhen, Xili, Nanshan, Shenzhen, Guangdong Province, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhidong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082, Guangdong Province, China; Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, 510000, Guangdong Province, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,10,10]]},"reference":[{"key":"ref1","series-title":"Appl. Math. Ser. 55","volume-title":"National Bureau Stand","author":"Abramowitz M.","year":"1964"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/27\/2\/025007"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/28\/7\/075009"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/21\/1\/005"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/28\/6\/065015"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/16\/3\/312"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/21M1409779"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.5540\/tcam.2022.023.03.00401"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0450(1972)011<0312:NMOAAD>2.0.CO;2"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/16\/3\/308"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/120880173"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/17\/5\/315"},{"key":"ref13","unstructured":"T. Hu, B. Jin, and Z. Zhou, Point Source Identification Using Singularity Enriched Neural Networks, https:\/\/arxiv.org\/abs\/2408.09143v1, 2024."},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/080712829"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2011.07.002"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2003.08.011"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1137\/22M1544257"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/abbc5d"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ac99f9"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/22\/4\/011"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.4208\/csiam-am.SO-2022-0052"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/accaa0"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/28\/6\/065018"},{"key":"ref24","unstructured":"K. Ren and Y. Zhong, Imaging Point Sources in Heterogeneous Environments, https:\/\/arxiv.org\/abs\/1901.07189v2, 2019."},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2022.03.041"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/19M1279915"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/978-88-7642-520-2_2"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ac88f3"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2023.112156"},{"key":"ref30","doi-asserted-by":"crossref","unstructured":"D. Zhang, Y. Chang, and Y. Guo, Jointly determining the point sources and obstacle from cauchy data, Inverse Problems,\u00a040 (2024) 015014, https:\/\/doi.org\/10.1088\/1361-6420\/ad10c8.","DOI":"10.1088\/1361-6420\/ad10c8"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/25M1725620","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:15:14Z","timestamp":1787224514000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M1725620"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,10]]},"references-count":30,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,10,31]]}},"alternative-id":["10.1137\/25M1725620"],"URL":"https:\/\/doi.org\/10.1137\/25m1725620","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,10]]}}}