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.