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The mathematics of varistors

Published online by Cambridge University Press:  19 May 2016

GIOVANNI CIMATTI
GIOVANNI CIMATTI*
Affiliation:
Department of Mathematics, University of Pisa, 56127, Pisa, Largo Bruno Pontecorvo 5, Italy email: [email protected]
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Abstract

A three-dimensional model of the varistor device is proposed. The thermal and electric conductivity of the material are taken to depend, in addition to the electric potential, on the temperature. Two theorems of existence and uniqueness of solutions for the boundary-value problem which determine the potential and the temperature inside the device are proposed. Levy–Caccioppoli global inversion theorem is used for the proof.

Keywords

varistornonlinear elliptic problemsexistenceuniqueness of solutionsLevy–Caccioppoli global inversion theorem
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 2 , April 2017 , pp. 208 - 220
Copyright
Copyright © Cambridge University Press 2016 

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References

[1] Ambrosetti, A. & Arcoya, D. (2011) An Introduction to Functional Analysis and Elliptic Problems, Birkhäuser, Boston.CrossRefGoogle Scholar
[2] Ambrosetti, A. & Prodi, G. (1973) Analisi Non Lineare, Quaderni S.N.S, Pisa.Google Scholar
[3] Caccioppoli, R. (1932) Sugli elementi uniti delle trasformazioni funzionali: Un teorema di esistenza e unicità e alcune sue applicazioni. Rend. Sem. Mat. Univ. Padova 3, 123–137.Google Scholar
[4] Chow, S. & Hale, J. K. (1982) Methods of Bifurcation Theory, Springer-Verlag, New York.CrossRefGoogle Scholar
[5] Cimatti, G. (2011) Remarks on the existence, uniqueness and semi-explicit solvability of systems of autonomous partial differential equations in divergence form with constant boundary conditions. Proc. R. Soc. Edim. 141, 481–495.CrossRefGoogle Scholar
[6] Data Sheets (1978) Nonlinear resistors, Philips. Amsterdam.Google Scholar
[7] Grondahl, L. O. & Geiger, P. H. (1927) A new electronic rectifier. Trans. AIEE 46, 357–366.Google Scholar
[8] Levy, P. (1920) Sur les fonctions de lignes implicites. Bull. Soc. Math. de France 48, 56–79.Google Scholar