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On one problem of electrophysics with discontinuous nonlinearity

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Abstract

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.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    D. K. Potapov

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  1. D. K. Potapov
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Correspondence to D. K. Potapov.

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Original Russian Text © D.K. Potapov, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 3, pp. 421–424.

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Potapov, D.K. On one problem of electrophysics with discontinuous nonlinearity. Diff Equat 50, 419–422 (2014). https://doi.org/10.1134/S0012266114030173

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  • DOI: https://doi.org/10.1134/S0012266114030173

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