Existence and uniqueness for the nonstationary problem of the electrical heating of a conductor due to the Joule-Thomson effect (Q1204361)

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.