The stationary thermistor problem with a current limiting device. (English) Zbl 0745.35042

(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.


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
Full Text: DOI


[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)
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