International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 125-138
doi:10.1155/S0161171293000158
Existence and uniqueness for the nonstationary problem of the electrical heating of a conductor due to the Joule-Thomson effect
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.
Abstract
Existence of a weak solution is established for the initial-boundary value problem for
the system ∂∂tu−div (θ(u)∇u)+σ(u)α(u)∇u∇v=σ(u)|∇v|2, div (σ(u)∇v)=0. The question of
uniqueness is also considered in some special cases.