Existence of a Weak Solution for the Phase Change Problem with Joule's Heating (Journal of Partial Differential Equations, 1994)
A phase change problem with Joule's heat ing describes tbe processes of electric heating in a conducting material. It is modeled as a coupled system of nonlinear partial differential equations with quadratic growth in the gradient. We establish the existence of a weak solution for the problem in two dimensions.
Keywords: phase change; system of nonlinear partial differential equations; quadratic growth