A two-dimensional stationary induction heating problem. (English) Zbl 0870.35034

Summary: We consider a system of equations modelling a steady-state induction heating process for ‘two-dimensional geometries’. Existence of a solution is stated in the Sobolev spaces \(W^{1,p}(\Omega)\) and is derived using Leray-Schauder’s fixed point theory.


35J60 Nonlinear elliptic equations
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[1] and , Asymptotic Analysis for Periodic Structures, North-Holland, London, 1978.
[2] Clain, Math. Meth. in the Appl. Sci. 3 pp 805– (1993)
[3] Conduction and Induction Heating, P. Peregrinus, London, 1990.
[4] and , Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977.
[5] Hong, SI AM J. Math. Anal. 22 pp 1491– (1991)
[6] Stampacchia, Comm. Pure Appl. Math. 16 pp 505– (1963)
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