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Zbl 0769.35059
Cimatti, Giovanni
Existence of weak solutions for the nonstationary problem of the Joule heating of a conductor. (English)
[J] Ann. Mat. Pura Appl., IV. Ser. 162, 33-42 (1992). ISSN 0373-3114; ISSN 1618-1891/e

The author considers an initial-boundary value problem for a system of two nonlinear partial differential equations using the Faedo-Galerkin method. The problem describes the electric heating of a conducting body. The main result is a theorem of existence of weak solutions for an arbitrarily large interval of time.
[N.Jacob (Erlangen)]
MSC 2000:
*35Q60 PDE of electromagnetic theory and optics
35D05 Existence of generalized solutions of PDE

Keywords: nonlinear elliptic-parabolic system; initial-boundary value problem; Faedo-Galerkin method

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