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On Regularization for Magneto-thermal Problems
  • Tao Chen,
  • Licheng Zhang,
  • Tong Kang
Tao Chen
Communication University of China
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Licheng Zhang
Communication University of China
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Tong Kang
Communication University of China
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Peer review status:UNDER REVIEW

28 Mar 2020Submitted to Mathematical Methods in the Applied Sciences
03 Apr 2020Assigned to Editor
03 Apr 2020Submission Checks Completed
05 Apr 2020Reviewer(s) Assigned

Abstract

This paper studies the magneto-thermal problems with the nonlinear material law. The main difficulty is to analysis the Joule heating term γ(u)| ∇×H|2. First, a regularized model is introduced. By time discretization, the well-posedness of the discrete problem is established, and the convergence of the solution as the time step size τ→0 is deduced. Finally, the solution to the regularized problem converges to the original as ε→0. The mathematical analysis of this paper provide a routine to obtain the well-posedness of the magneto-thermal problems and gives an answer to the open question from the previous work.