Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions
Author:
Giovanni Cimatti
Journal:
Quart. Appl. Math. 47 (1989), 117-121
MSC:
Primary 80A20; Secondary 78A99
DOI:
https://doi.org/10.1090/qam/987900
MathSciNet review:
987900
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Abstract: The steady-state electrical heating of a solid conductor is studied with mixed boundary conditions. A theorem of existence, nonexistence, and uniqueness of solutions is given under general assumptions on the electrical and thermal conductivities. The basic tool of the proof is a transformation first proposed in [3] by H. Diesselhorst.
- Giovanni Cimatti, A bound for the temperature in the thermistor problem, IMA J. Appl. Math. 40 (1988), no. 1, 15–22. MR 983747, DOI https://doi.org/10.1093/imamat/40.1.15
- 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
H. Diesselhorst, Ueber das Probleme eines elektrisch erwärmten Leiters, Ann. Physics 1, 312–325 (1900)
F. Kohlrausch, Ueber den stationären Temperature-zustand eines elektrisch geheizten Leiters, Ann. Physics 1, 132–158 (1900)
- Sam Howison, A note on the thermistor problem in two space dimensions, Quart. Appl. Math. 47 (1989), no. 3, 509–512. MR 1012273, DOI https://doi.org/10.1090/qam/1012273
G. Cimatti, A bound for the temperature in the thermistor problem, IMA J. Appl. Math. 40, 15–22 (1988)
G. Cimatti and G. Prodi, Existence results for a nonlinear elliptic system modelling a temperature dependent electrical resistor, Ann. Mat. Pura Appl., to appear
H. Diesselhorst, Ueber das Probleme eines elektrisch erwärmten Leiters, Ann. Physics 1, 312–325 (1900)
F. Kohlrausch, Ueber den stationären Temperature-zustand eines elektrisch geheizten Leiters, Ann. Physics 1, 132–158 (1900)
S. D. Howison, A note on the thermistor problem in two space dimensions, Quart. Appl. Math. 47 (1989), to appear
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Article copyright:
© Copyright 1989
American Mathematical Society