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

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.