{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:16:26Z","timestamp":1762431386039},"reference-count":31,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We are concerned with the wave propagation in a homogeneous 2D or 3D membrane \u03a9 of finite size. We assume that either the membrane is initially at rest or we know its initial shape\n(but not necessarily both) and its boundary is subject to a known boundary force.\nWe address the question of estimating the needed time-dependent body force to exert on the membrane to reach\na desired state at a given final time <jats:italic>T<\/jats:italic>. As an additional information, we ask for\nthe displacement on the boundary. We consider the displacement either at a single point of the boundary or on the whole boundary.\nFirst, we show the uniqueness of solution of these inverse problems under natural conditions on the final time <jats:italic>T<\/jats:italic>. If, in addition, the displacement on the whole boundary is only time dependent (which means that the boundary moves with a constant speed), this condition on <jats:italic>T<\/jats:italic> is removed if \u03a9 satisfies Schiffer\u2019s property.\nSecond, we derive a conditional H\u00f6lder stability inequality for estimating such a time-dependent force. Third, we propose a numerical procedure based on the application of the satisfier function along with the standard Fourier expansion of the solution to the problems. Numerical tests are given to illustrate the applicability of the proposed procedure.<\/jats:p>","DOI":"10.1515\/cmam-2017-0061","type":"journal-article","created":{"date-parts":[[2017,12,22]],"date-time":"2017-12-22T22:16:40Z","timestamp":1513981000000},"page":"323-339","source":"Crossref","is-referenced-by-count":3,"title":["Estimation of the Time-Dependent Body Force Needed to Exert on a Membrane to Reach a Desired State at the Final Time"],"prefix":"10.1515","volume":"19","author":[{"given":"Lyubomir","family":"Boyadjiev","sequence":"first","affiliation":[{"name":"Department of Mathematics , Faculty of Sciences , Kuwait University Safate , Kuwait City , Kuwait"}]},{"given":"Kamal","family":"Rashedi","sequence":"additional","affiliation":[{"name":"Department of Mathematics , University of Science and Technology of Mazandaran , Behshahr , Iran"}]},{"given":"Mourad","family":"Sini","sequence":"additional","affiliation":[{"name":"RICAM , Austrian Academy of Sciences , Altenbergerstr. 69, A-4040 , Linz , Austria"}]}],"member":"374","published-online":{"date-parts":[[2017,12,22]]},"reference":[{"key":"2023033110021991214_j_cmam-2017-0061_ref_001_w2aab3b7d275b1b6b1ab2b1b1Aa","unstructured":"M.  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Appl. 90,\nSpringer, New York, 1997.","DOI":"10.1007\/978-1-4612-1878-4"},{"key":"2023033110021991214_j_cmam-2017-0061_ref_004_w2aab3b7d275b1b6b1ab2b1b4Aa","doi-asserted-by":"crossref","unstructured":"R.  Dalmasso,\nA note on the Schiffer conjecture,\nHokkaido Math. J. 28 (1999), no. 2, 373\u2013383.","DOI":"10.14492\/hokmj\/1351001220"},{"key":"2023033110021991214_j_cmam-2017-0061_ref_005_w2aab3b7d275b1b6b1ab2b1b5Aa","doi-asserted-by":"crossref","unstructured":"J.  Deng,\nSome results on the Schiffer conjecture in R2R^{2},\nJ. Differential Equations 253 (2012), no. 8, 2515\u20132526.","DOI":"10.1016\/j.jde.2012.06.002"},{"key":"2023033110021991214_j_cmam-2017-0061_ref_006_w2aab3b7d275b1b6b1ab2b1b6Aa","doi-asserted-by":"crossref","unstructured":"H. W.  Engl, O.  Scherzer and M.  Yamamoto,\nUniqueness and stable determination of forcing terms in linear partial differential equations with overspecified boundary data,\nInverse Problems 10 (1994), no. 6, 1253\u20131276.","DOI":"10.1088\/0266-5611\/10\/6\/006"},{"key":"2023033110021991214_j_cmam-2017-0061_ref_007_w2aab3b7d275b1b6b1ab2b1b7Aa","doi-asserted-by":"crossref","unstructured":"P. C.  Hansen,\nAnalysis of discrete ill-posed problems by means of the \ud835\uddab{\\sf L}-curve,\nSIAM Rev. 34 (1992), no. 4, 561\u2013580.","DOI":"10.1137\/1034115"},{"key":"2023033110021991214_j_cmam-2017-0061_ref_008_w2aab3b7d275b1b6b1ab2b1b8Aa","doi-asserted-by":"crossref","unstructured":"A.  Hazanee, M. I.  Ismailov, D.  Lesnic and N. B.  Kerimov,\nAn inverse time-dependent source problem for the heat equation,\nAppl. Numer. Math. 69 (2013), 13\u201333.","DOI":"10.1016\/j.apnum.2013.02.004"},{"key":"2023033110021991214_j_cmam-2017-0061_ref_009_w2aab3b7d275b1b6b1ab2b1b9Aa","doi-asserted-by":"crossref","unstructured":"S. O.  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Sci. 365,\nKluwer Academic Publisher, Dordrecht (1992), 185\u2013194.","DOI":"10.1007\/978-94-011-2436-2_17"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/19\/2\/article-p323.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2017-0061\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2017-0061\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T10:45:42Z","timestamp":1680259542000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2017-0061\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,22]]},"references-count":31,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2,24]]},"published-print":{"date-parts":[[2019,4,1]]}},"alternative-id":["10.1515\/cmam-2017-0061"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2017-0061","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2017,12,22]]}}}