On a Steady-State Two-Phase Stefan Problem with Extraction
José Francisco Rodrigues · Birkhäuser Basel eBooks · 1990
In this note we show that the steady-state free boundary of a two-phase Stefan problem of continuous casting type, in two dimensions, is given by a Lipschitz curve. We establish the stability of this curve with respect to the lateral cooling. This is applied to solve an optimal control problem with observation of the free boundary. Finally we describe briefly the derivation of an asymptotic model for high velocities of extraction.