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Existence of weak solutions for the nonstationary problem of the Joule heating of a conductor. (English) Zbl 0769.35059

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.
Reviewer: N.Jacob (Erlangen)

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
35D05 Existence of generalized solutions of PDE (MSC2000)
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