Clain, StĂ©phane; Touzani, Rachid A two-dimensional stationary induction heating problem. (English) Zbl 0870.35034 Math. Methods Appl. Sci. 20, No. 9, 759-766 (1997). 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. Cited in 4 Documents MSC: 35J60 Nonlinear elliptic equations Keywords:existence; Leray-Schauder’s fixed point theory PDF BibTeX XML Cite \textit{S. Clain} and \textit{R. Touzani}, Math. Methods Appl. Sci. 20, No. 9, 759--766 (1997; Zbl 0870.35034) Full Text: DOI OpenURL References: [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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.