Parietti, C.; Rappaz, J. A quasi-static two-dimensional induction heating problem. I: Modelling and analysis. (English) Zbl 1010.80002 Math. Models Methods Appl. Sci. 8, No. 6, 1003-1021 (1998). Under the conditions exposed in the review of Part II (Zbl 1010.80004) the authors here show the existence of a weak solution to the problem and under additional assumptions they also study uniqueness of the solution. Cited in 5 Documents MSC: 80A20 Heat and mass transfer, heat flow (MSC2010) 78A25 Electromagnetic theory (general) Keywords:nonlinear elliptic-parabolic system; induction heating process; Joule effect; sinusoidal electromagnetic field Citations:Zbl 1010.80004 PDFBibTeX XMLCite \textit{C. Parietti} and \textit{J. Rappaz}, Math. Models Methods Appl. Sci. 8, No. 6, 1003--1021 (1998; Zbl 1010.80002) Full Text: DOI