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A bound for the temperature in the thermistor problem. (English) Zbl 0694.35139

Summary: With a suitable transformation an upper bound for the temperature is given in the thermistor problem when the electrical conductivity is bounded. Using a fixed-point argument the new formulation leads to the proof of a theorem that at least one solution exists.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35J70 Degenerate elliptic equations
74A15 Thermodynamics in solid mechanics
47H10 Fixed-point theorems
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