{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T04:15:52Z","timestamp":1727928952422},"reference-count":20,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider an inverse problem for the Helmholtz equation of reconstructing a solution from measurements taken on a segment inside a semi-infinite strip.\nHomogeneous Neumann conditions are prescribed on both side boundaries of the strip and an unknown Dirichlet condition on the remaining part of the boundary.\nAdditional complexity is that the radiation condition at infinity is unknown.\nOur aim is to find the unknown function in the Dirichlet boundary condition and the radiation condition.\nSuch problems appear in acoustics to determine acoustical sources and surface vibrations from acoustic field measurements.\nThe problem is split into two sub-problems, a well-posed and an ill-posed problem.\nWe analyse the theoretical properties of both problems; in particular, we show that the radiation condition is described by a stable non-linear problem.\nThe second problem is ill-posed, and we use the Landweber iteration method together with the discrepancy principle to regularize it.\nNumerical tests show that the approach works well.<\/jats:p>","DOI":"10.1515\/cmam-2022-0244","type":"journal-article","created":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T12:41:11Z","timestamp":1690202471000},"page":"813-828","source":"Crossref","is-referenced-by-count":1,"title":["Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior Segment"],"prefix":"10.1515","volume":"24","author":[{"given":"Pauline","family":"Achieng","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics , University of Nairobi , P.O. Box 30197 , Nairobi , Kenya ; and Department of Mathematics, Link\u00f6ping University, SE-581 83 Link\u00f6ping, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fredrik","family":"Berntsson","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Link\u00f6ping University , SE-581 83 Link\u00f6ping , Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladimir","family":"Kozlov","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Link\u00f6ping University , SE-581 83 Link\u00f6ping , Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,7,25]]},"reference":[{"key":"2024100217254196163_j_cmam-2022-0244_ref_001","doi-asserted-by":"crossref","unstructured":"P. Achieng, F. Berntsson, J. Chepkorir and V. Kozlov,\nAnalysis of Dirichlet\u2013Robin iterations for solving the Cauchy problem for elliptic equations,\nBull. Iranian Math. 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Turesson,\nAn alternating iterative procedure for the Cauchy problem for the Helmholtz equation,\nInverse Probl. Sci. Eng. 22 (2014), no. 1, 45\u201362.","DOI":"10.1080\/17415977.2013.827181"},{"key":"2024100217254196163_j_cmam-2022-0244_ref_005","doi-asserted-by":"crossref","unstructured":"F. Berntsson, V. A. Kozlov, L. Mpinganzima and B. O. Turesson,\nRobin\u2013Dirichlet algorithms for the Cauchy problem for the Helmholtz equation,\nInverse Probl. Sci. Eng. 26 (2018), no. 7, 1062\u20131078.","DOI":"10.1080\/17415977.2017.1380639"},{"key":"2024100217254196163_j_cmam-2022-0244_ref_006","doi-asserted-by":"crossref","unstructured":"J. Cheng, V. Isakov and S. Lu,\nIncreasing stability in the inverse source problem with many frequencies,\nJ. Differential Equations 260 (2016), no. 5, 4786\u20134804.","DOI":"10.1016\/j.jde.2015.11.030"},{"key":"2024100217254196163_j_cmam-2022-0244_ref_007","doi-asserted-by":"crossref","unstructured":"D. Colton and R. 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