Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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.

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

  • [1] G. Cimatti, A bound for the temperature in the thermistor problem, IMA J. Appl. Math. 40, 15-22 (1988) MR 983747
  • [2] G. Cimatti and G. Prodi, Existence results for a nonlinear elliptic system modelling a temperature dependent electrical resistor, Ann. Mat. Pura Appl., to appear MR 980982
  • [3] H. Diesselhorst, Ueber das Probleme eines elektrisch erwärmten Leiters, Ann. Physics 1, 312-325 (1900)
  • [4] F. Kohlrausch, Ueber den stationären Temperature-zustand eines elektrisch geheizten Leiters, Ann. Physics 1, 132-158 (1900)
  • [5] S. D. Howison, A note on the thermistor problem in two space dimensions, Quart. Appl. Math. 47 (1989), to appear MR 1012273

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DOI: https://doi.org/10.1090/qam/987900
Article copyright: © Copyright 1989 American Mathematical Society

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