Cimatti, Giovanni The stationary thermistor problem with a current limiting device. (English) Zbl 0745.35042 Proc. R. Soc. Edinb., Sect. A 116, No. 1-2, 79-84 (1990). (Author’s summary.) The electrical heating of a conductor connected with a current limiting device of total resistance \(R\) is studied under mixed boundary conditions. A theorem of existence is given using a transformation which permits the reduction of the nonlinear system governing the problem to the classical mixed boundary value problem for the Laplace equation. Reviewer: G.A.Sokhadze (Kutaisi) Cited in 12 Documents MSC: 35Q60 PDEs in connection with optics and electromagnetic theory 78A30 Electro- and magnetostatics 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 74F15 Electromagnetic effects in solid mechanics Keywords:existence; mixed boundary value problem; Laplace equation PDF BibTeX XML Cite \textit{G. Cimatti}, Proc. R. Soc. Edinb., Sect. A, Math. 116, No. 1--2, 79--84 (1990; Zbl 0745.35042) Full Text: DOI OpenURL References: [1] DOI: 10.1002/andp.19003060211 · JFM 31.0808.01 [2] Cimatti, Quart. Appl. Math. XLVII pp 117– (1989) · Zbl 0694.35137 [3] DOI: 10.1002/andp.19003060107 · JFM 31.0807.02 [4] Protter, Maximum principle in partial differential equations (1967) 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.