Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

On two problems of electrical heating of conductors


Author: Giovanni Cimatti
Journal: Quart. Appl. Math. 49 (1991), 729-740
MSC: Primary 78A25; Secondary 35Q60, 80A20
DOI: https://doi.org/10.1090/qam/1134748
MathSciNet review: MR1134748
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The thermal effects of the currents induced in a massive conductor by an external slowly varying magnetic field are studied with regard to existence and uniqueness of solutions. In the first part a theorem of existence of solution is also given for the thermistor problem with a current limiting device.


References [Enhancements On Off] (What's this?)

  • [1] G. Cimatti, The stationary thermistor problem with a current limiting device, Proc. Roy. Soc. Edinburgh Sect. 116A, 79-84 (1990) MR 1076354
  • [2] G. Cimatti and G. Prodi, Existence results for a nonlinear elliptic system modelling a temperature dependent electrical resistor, Ann. Mat. Pura Appl. 62, 227-236 (1988) MR 980982
  • [3] A. C. Fowler, S. D. Howison, and E. J. Hinch, Temperature surges in current-limiting circuit devices, to appear
  • [4] H. A. Haus and J. R. Melcher, Electromagnetic Fields and Energy, Prentice-Hall, Englewood Cliffs, NJ, 1989
  • [5] O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Ural'ceva, Linear and quasilinear equations of parabolic type, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968 MR 0241822
  • [6] J. L. Lions, Equations Différentielles Operationelles et Problémes aux Limites, Springer-Verlag, Berlin, 1961 MR 0153974
  • [7] M. H. Protter and H. F. Weinberger, Maximum Principle in Partial Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967 MR 0219861

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 78A25, 35Q60, 80A20

Retrieve articles in all journals with MSC: 78A25, 35Q60, 80A20


Additional Information

DOI: https://doi.org/10.1090/qam/1134748
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society