On the steady-state continuous casting Stefan problem with nonlinear cooling
Michel Marie Chipot, José Francisco Rodrigues · Quarterly of Applied Mathematics · 1983
A steady-state one-phase Stefan problem corresponding to the solidification process of an ingot of pure metal by continuous casting with nonlinear lateral cooling is considered via the weak formulation introduced in [5] for the dam problem. Two existence results are obtained, for a general nonlinear flux and for a maximal monotone flux. Comparison results and the regularity of the free boundary are discussed. An uniqueness theorem is given for the monotone case.