Asymptotic Convergences in a One-Phase Continuous-Casting Stefan Problem with High Extraction Velocity

Asymptotic convergence for variational solutions and for thefree boundaries in a one-phase continuous-casting problem ofthe Stefan type are derived when the Péclet number ß+. This corresponds, in particular, to a model with high extractionvelocity, where an ultraparabolic problem is obtained from aparabolic one and, in the stabilized case (i.e. when t +), aparabolic problem results from an elliptic one. The asymptoticstabilization in time as t + is also discussed in the limitß = +.