Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions

Cimatti, Giovanni

doi:10.1090/qam/987900

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.

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