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