{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,7]],"date-time":"2024-07-07T21:53:12Z","timestamp":1720389192919},"reference-count":23,"publisher":"Elsevier BV","issue":"7","license":[{"start":{"date-parts":[[2010,12,1]],"date-time":"2010-12-01T00:00:00Z","timestamp":1291161600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2010,12]]},"DOI":"10.1016\/j.amc.2010.09.019","type":"journal-article","created":{"date-parts":[[2010,9,21]],"date-time":"2010-09-21T08:32:12Z","timestamp":1285057932000},"page":"2913-2922","source":"Crossref","is-referenced-by-count":16,"title":["A note on a Cauchy problem for the Laplace equation: Regularization and error estimates"],"prefix":"10.1016","volume":"217","author":[{"given":"Nguyen Huy","family":"Tuan","sequence":"first","affiliation":[]},{"given":"Dang Duc","family":"Trong","sequence":"additional","affiliation":[]},{"given":"Pham Hoang","family":"Quan","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.amc.2010.09.019_b0005","first-page":"3236","article-title":"Regularization of an ill-posed Cauchy problem for evolution equations in a Banach space","author":"Abdulkerimov","year":"1977","journal-title":"Azerbaidzan. Gos. Univ. Ucen. Zap., Fiz. i Mat."},{"key":"10.1016\/j.amc.2010.09.019_b0015","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1137\/0112025","article-title":"Error estimates for some unstable continuation problems","volume":"12","author":"Cannon","year":"1964","journal-title":"J. Soc. Industr. Appl. Math."},{"key":"10.1016\/j.amc.2010.09.019_b0020","first-page":"87","article-title":"Some problems in numerical analytic continuation","volume":"2","author":"Cannon","year":"1965","journal-title":"SIAM Numer. Anal."},{"issue":"2","key":"10.1016\/j.amc.2010.09.019_b0025","first-page":"64","article-title":"Approximation of Cauchy problems for elliptic equations using the method of lines","volume":"4","author":"Charton","year":"2005","journal-title":"WSEAS Trans. Math."},{"issue":"5","key":"10.1016\/j.amc.2010.09.019_b0035","doi-asserted-by":"crossref","DOI":"10.1088\/0266-5611\/25\/5\/055002","article-title":"A non-local boundary value problem method for the Cauchy problem for elliptic equations","volume":"25","author":"Hao","year":"2009","journal-title":"Inverse Problems"},{"key":"10.1016\/j.amc.2010.09.019_b0040","first-page":"80515","article-title":"A non-local boundary value problem method for parabolic equations backward in time","volume":"345","author":"Hao","year":"2008","journal-title":"J. Math. Anal. Appl."},{"issue":"6","key":"10.1016\/j.amc.2010.09.019_b0045","doi-asserted-by":"crossref","first-page":"2187","DOI":"10.1137\/S1064827597331394","article-title":"Wavelet and Fourier method for solving the sideways heat equation","volume":"21","author":"Elden","year":"2000","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.amc.2010.09.019_b0050","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.mcm.2005.08.003","article-title":"Fourier regularization method for solving the surface heat flux from interior observations","volume":"42","author":"Fu","year":"2005","journal-title":"Math. Comput. Model."},{"key":"10.1016\/j.amc.2010.09.019_b0055","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.cam.2003.10.011","article-title":"Simplified Tikhonov and Fourier regularization methods on a general sideways parabolic equation","volume":"167","author":"Fu","year":"2004","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.amc.2010.09.019_b0060","series-title":"Ill-Posed Problems in the Natural Science","first-page":"89","article-title":"Inverse problems in the gravimetry and magnetometry","author":"Glasko","year":"1987"},{"key":"10.1016\/j.amc.2010.09.019_b0075","series-title":"Inverse Problems for Partial Differential Equations","author":"Isakov","year":"2006"},{"key":"10.1016\/j.amc.2010.09.019_b0080","series-title":"Operator-Differential Equations and Ill-Posed Problems","author":"Ivanov","year":"1995"},{"key":"10.1016\/j.amc.2010.09.019_b0085","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.cam.2005.04.031","article-title":"Fourth-order modified method for the Cauchy problem for the Laplace equation","volume":"192","author":"Qian","year":"2006","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"10.1016\/j.amc.2010.09.019_b0090","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.jmaa.2007.05.040","article-title":"Two regularization methods for a Cauchy problem for the Laplace equation","volume":"338","author":"Qian","year":"2008","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.amc.2010.09.019_b0095","series-title":"Ill-Posed Problems in Mathematical Physics and Analysis","author":"Lavrentev","year":"1986"},{"key":"10.1016\/j.amc.2010.09.019_b0100","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1002\/(SICI)1097-0207(19981015)43:3<479::AID-NME430>3.0.CO;2-D","article-title":"The boundary element solution of the Laplace and biharmonic equations subjected to noisy boundary data","volume":"43","author":"Lesnic","year":"1998","journal-title":"Int. J. Numer. Meth. Eng."},{"key":"10.1016\/j.amc.2010.09.019_b0105","series-title":"Abstract Cauchy Problems: Three Approaches","author":"Melnikova","year":"2001"},{"key":"10.1016\/j.amc.2010.09.019_b0120","unstructured":"G.T. Symm, R.A. Pitfield, Solution of Laplaces Equation in Two Dimensions, NPL Report NAC44, 1974."},{"key":"10.1016\/j.amc.2010.09.019_b0125","doi-asserted-by":"crossref","first-page":"961","DOI":"10.4171\/ZAA\/740","article-title":"Optimal stable solution of Cauchy problems for elliptic equations","volume":"15","author":"Tautenhahn","year":"1996","journal-title":"Z. Anal. Anwendungen"},{"key":"10.1016\/j.amc.2010.09.019_b0130","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1080\/01630569808816834","article-title":"Optimality for ill-posed problems under general source conditions","volume":"19","author":"Tautenhahn","year":"1998","journal-title":"Numer. Funct. Anal. Optim."},{"key":"10.1016\/j.amc.2010.09.019_b0135","first-page":"1","article-title":"Remarks on a 2-D nonlinear backward heat problem using a truncated fourier series method","volume":"2009","author":"Trong","year":"2009","journal-title":"Electron. J. Diff. Eqns."},{"key":"10.1016\/j.amc.2010.09.019_b0150","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1007\/BF00861941","article-title":"Regularization of nonstationary problems for elliptic equations","volume":"65","author":"Vabishchevich","year":"1993","journal-title":"J. Eng. Phys. Thermophys."},{"key":"10.1016\/j.amc.2010.09.019_b0155","article-title":"A method of numerical solution of the Cauchy problem for elliptic equations","volume":"38","author":"Vabishchevich","year":"1984","journal-title":"Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet."}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300310009665?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300310009665?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T23:57:53Z","timestamp":1544227073000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300310009665"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12]]},"references-count":23,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["S0096300310009665"],"URL":"http:\/\/dx.doi.org\/10.1016\/j.amc.2010.09.019","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2010,12]]}}}