International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 125-138

Existence and uniqueness for the nonstationary problem of the electrical heating of a conductor due to the Joule-Thomson effect

Xiangsheng Xu

Department of Mathematical Sciences, 301 Science-Engineering Building, University of Arkansas, Fayetteville 72701, Arkansas, USA

Received 15 August 1991; Revised 10 April 1992

Copyright © 1993 Xiangsheng Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Existence of a weak solution is established for the initial-boundary value problem for the system tudiv (θ(u)u)+σ(u)α(u)uv=σ(u)|v|2, div (σ(u)v)=0. The question of uniqueness is also considered in some special cases.