{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:18:14Z","timestamp":1760231894874,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T00:00:00Z","timestamp":1665360000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11961044","11561045"],"award-info":[{"award-number":["11961044","11561045"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we investigate a spherically symmetric inverse heat conduction problem, which determines the internal surface temperature distribution of the hollow sphere from measured data at the fixed location inside it. This problem is ill-posed, and a conditional stability result of its solution is given. A modified quasi-boundary value method is proposed to solve the ill-posed problem. Two Ho\u00a8lder-type error estimates between the approximation solution and its exact solution are obtained under an a priori and an a posteriori regularization parameter selection rule, respectively.<\/jats:p>","DOI":"10.3390\/sym14102102","type":"journal-article","created":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T03:32:56Z","timestamp":1665459176000},"page":"2102","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Modified Regularization Method for a Spherically Symmetric Inverse Heat Conduction Problem"],"prefix":"10.3390","volume":"14","author":[{"given":"Wei","family":"Cheng","sequence":"first","affiliation":[{"name":"College of Science, Henan University of Technology, Zhengzhou 450001, China"}]},{"given":"Yi-Liang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Air Transport and Engineering, Nanhang Jincheng College, Nanjing 211156, China"}]},{"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou 730050, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,10]]},"reference":[{"key":"ref_1","unstructured":"Beck, J.V., Blackwell, B., and Clair, S.R. 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