{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:39Z","timestamp":1740134559271,"version":"3.37.3"},"reference-count":13,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171136","11261032","Q201015"],"award-info":[{"award-number":["11171136","11261032","Q201015"]}],"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":["11171136","11261032","Q201015"],"award-info":[{"award-number":["11171136","11261032","Q201015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Distinguished Young Scholars Fund of Lanzhou University of Technology","award":["11171136","11261032","Q201015"],"award-info":[{"award-number":["11171136","11261032","Q201015"]}]},{"name":"Gansu Province College","award":["11171136","11261032","Q201015"],"award-info":[{"award-number":["11171136","11261032","Q201015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the quasireversibility regularization method. Convergence estimate is presented between the exact solution and the regularization solution. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.<\/jats:p>","DOI":"10.1155\/2013\/245963","type":"journal-article","created":{"date-parts":[[2013,4,24]],"date-time":"2013-04-24T17:01:02Z","timestamp":1366822862000},"page":"1-8","source":"Crossref","is-referenced-by-count":3,"title":["The Quasireversibility Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation"],"prefix":"10.1155","volume":"2013","author":[{"given":"Xiao-Xiao","family":"Li","sequence":"first","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/14\/3\/010"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s10665-005-9023-0"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2002.11.025"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.enganabound.2007.08.002"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.09.001"},{"issue":"2","key":"2","first-page":"665","volume":"211","year":"2006","journal-title":"Journal of Computational Physics"},{"issue":"2","key":"3","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1088\/0266-5611\/3\/2\/009","volume":"3","year":"1987","journal-title":"Inverse Problems"},{"issue":"11","key":"12","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.1016\/0017-9310(81)90144-7","volume":"24","year":"1981","journal-title":"International Journal of Heat and Mass Transfer"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.04.059"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1080\/17415970600725128"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.12.033"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.04.031"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.07.055"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/245963.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/245963.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/245963.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T07:57:28Z","timestamp":1498031848000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/245963\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":13,"alternative-id":["245963","245963"],"URL":"https:\/\/doi.org\/10.1155\/2013\/245963","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}