Vol. 12, No. 1, 2019
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Analytical solution of a one-dimensional thermistor problem with Robin boundary condition

Volodymyr Hrynkiv and Alice Turchaninova

Vol. 12 (2019), No. 1, 79–88
DOI: 10.2140/involve.2019.12.79
Abstract

A one-dimensional nonlinear heat conduction equation of steady-state Joule heating in the presence of an electric field in a metal with temperature-dependent conductivities is considered. A technique developed by Young (1986) is adapted and used to derive an analytical solution for the problem with a Robin boundary condition.

Keywords
thermistor problem, Robin boundary condition, Joule heating, analytical solution
Mathematical Subject Classification 2010
Primary: 35J60
Milestones
Received: 26 April 2017
Revised: 5 October 2017
Accepted: 14 February 2018
Published: 31 May 2018

Communicated by Suzanne Lenhart
Authors
Volodymyr Hrynkiv
Department of Mathematics and Statistics
University of Houston - Downtown
Houston, TX
United States
Alice Turchaninova
University of Houston - Downtown
Houston, TX
United States