On one problem of electrophysics with discontinuous nonlinearity

We consider a conductor heating problem in the following setting: a constant voltage and a constant temperature are maintained on the conductor surface, and the electric conductivity of the material experiences jumps when passing through certain temperatures. Earlier-obtained results for problems wi...

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Bibliographic Details
Published in:Differential equations 2014-03, Vol.50 (3), p.419-422
Main Author: Potapov, D. K.
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Differential equations
Inequality
Mathematical models
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Short Communications
Studies
Temperature
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Summary:We consider a conductor heating problem in the following setting: a constant voltage and a constant temperature are maintained on the conductor surface, and the electric conductivity of the material experiences jumps when passing through certain temperatures. Earlier-obtained results for problems with a spectral parameter for equations of elliptic type with discontinuous nonlinearities are applied to this problem of electrophysics. We weaken the conditions imposed on the set of points of discontinuity of the nonlinearity (the electric conductivity of the conductor) occurring in the equation.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266114030173