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
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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.
- Giovanni Cimatti, The stationary thermistor problem with a current limiting device, Proc. Roy. Soc. Edinburgh Sect. A 116 (1990), no. 1-2, 79–84. MR 1076354, DOI https://doi.org/10.1017/S0308210500031383
- Giovanni Cimatti and Giovanni Prodi, Existence results for a nonlinear elliptic system modelling a temperature dependent electrical resistor, Ann. Mat. Pura Appl. (4) 152 (1988), 227–236. MR 980982, DOI https://doi.org/10.1007/BF01766151
A. C. Fowler, S. D. Howison, and E. J. Hinch, Temperature surges in current-limiting circuit devices, to appear
H. A. Haus and J. R. Melcher, Electromagnetic Fields and Energy, Prentice-Hall, Englewood Cliffs, NJ, 1989
- O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural′ceva, Lineĭ nye i kvazilineĭ nye uravneniya parabolicheskogo tipa, Izdat. “Nauka”, Moscow, 1967 (Russian). MR 0241821
- J.-L. Lions, Équations différentielles opérationnelles et problèmes aux limites, Die Grundlehren der mathematischen Wissenschaften, Bd. 111, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961 (French). MR 0153974
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
G. Cimatti, The stationary thermistor problem with a current limiting device, Proc. Roy. Soc. Edinburgh Sect. 116A, 79–84 (1990)
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)
A. C. Fowler, S. D. Howison, and E. J. Hinch, Temperature surges in current-limiting circuit devices, to appear
H. A. Haus and J. R. Melcher, Electromagnetic Fields and Energy, Prentice-Hall, Englewood Cliffs, NJ, 1989
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
J. L. Lions, Equations Différentielles Operationelles et Problémes aux Limites, Springer-Verlag, Berlin, 1961
M. H. Protter and H. F. Weinberger, Maximum Principle in Partial Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967
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Article copyright:
© Copyright 1991
American Mathematical Society
