Vol. 12, No. 1, 2019
Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 6, 901–1080
Issue 5, 721–899
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
Contacts
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Other MSP Journals
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