On an induction–conduction PDEs system in the harmonic regime

A space-time discretization for an electromagnetic problem with moving non-magnetic conductor

“…Another common treatment is incorporating the Coulomb gauge in the formulation (cf. [8,9]), which is done by appending the following penalty term to the left-hand side (LHS) of the relation ( 5)…”

Analysis of a non-uniformly elliptic and nonlinear coupled parabolic–elliptic system arising in steel hardening

“…It can be seen in [12] that there exists a weak solution (ϕ k , A k , θ k ) to the system (36)-( 43) such that…”

“…Nevertheless, our main concern lies on the mathematical analysis of the industrial heating process described in terms of the harmonic regime. This problem was studied in [12] under more restrictive assumptions on data, but now we consider more realistic hypotheses on the electric conductivity σ 0 , namely σ 0 is non-uniformly elliptic. As a result from the mathematical standpoint, we have to deal with a much more complex problem.…”

Analysis and simulations of multifrequency induction hardening

“…In two recent papers the simpler frequency domain situation of Joule heating has been studied. In [8] the Boccardo-Galluet approach has been used to prove existence of a weak solution, while in [4] new regularity results established in [3] have been used to prove existence and stability in the frequency domain setting. In [11,12] the eddy current model has been considered in the time domain.…”