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The coupling between them is provided through the temperature-dependent electric conductivity. The behavior of the material is defined by an anhysteretic \ud835\udc6f-\ud835\udc69 curve. The magnetic flux across a meridian section of the medium gives rise to the magnetic field equation with the unknown nonlocal boundary condition. We present a variational formulation for this coupling problem and prove its solvability in terms of the Rothe method. The nonlinearity is handled by the theory of monotone operators. We also suggest a discrete decoupled scheme to solve this problem by employing the finite element method and show some numerical results in the final section.<\/jats:p>","DOI":"10.1515\/cmam-2022-0093","type":"journal-article","created":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T12:41:46Z","timestamp":1686746506000},"page":"239-264","source":"Crossref","is-referenced-by-count":0,"title":["A Formulation for a Nonlinear Axisymmetric Magneto-Heat Coupling Problem with an Unknown Nonlocal Boundary Condition"],"prefix":"10.1515","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4204-4576","authenticated-orcid":false,"given":"Ran","family":"Wang","sequence":"first","affiliation":[{"name":"School of Data Science and Media Intelligence , Communication University of China ; and Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences , Beijing , 100049 , P. R. China"}]},{"given":"Huai","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Computational Geodynamics , University of Chinese Academy of Sciences , Beijing , 100049 , P. R. China"}]},{"given":"Tong","family":"Kang","sequence":"additional","affiliation":[{"name":"School of Data Science and Media Intelligence , Communication University of China ; and Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences , Beijing , 100049 , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2023,6,15]]},"reference":[{"key":"2024010712054153814_j_cmam-2022-0093_ref_001","doi-asserted-by":"crossref","unstructured":"G. Akrivis and S. Larsson, Linearly implicit finite element methods for the time-dependent Joule heating problem, BIT 45 (2005), no. 3, 429\u2013442.","DOI":"10.1007\/s10543-005-0008-1"},{"key":"2024010712054153814_j_cmam-2022-0093_ref_002","doi-asserted-by":"crossref","unstructured":"J. Barglik, I. 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