## 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.

### 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
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### 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)
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