Xu, Xiangsheng Existence and uniqueness for the nonstationary problem of the electrical heating of a conductor due to the Joule-Thomson effect. (English) Zbl 0801.35008 Int. J. Math. Math. Sci. 16, No. 1, 125-138 (1993). Summary: Existence of a weak solution is established for the initial-boundary value problem for the system \[ {\partial\over \partial t} u- \text{div}(\Theta(u)\nabla u)+ \sigma(u)\alpha(u)\nabla u\nabla v= \sigma(u)|\nabla v|^ 2,\quad \text{div}(\sigma(u)\nabla v)= 0. \] The question of uniqueness is also considered in some special cases. Cited in 4 Documents MSC: 35D05 Existence of generalized solutions of PDE (MSC2000) 35D10 Regularity of generalized solutions of PDE (MSC2000) 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations Keywords:Joule-Thomson effect; quadratic gradient growth PDFBibTeX XMLCite \textit{X. Xu}, Int. J. Math. Math. Sci. 16, No. 1, 125--138 (1993; Zbl 0801.35008) Full Text: DOI EuDML