Abstract
A simplified model for the solidification of an ingot being cast continuously by withdrawing it from a mould at constant rate is studied via the variational inequalities approach. Existence, uniqueness and regularity results are given for this one-phase Stefan type problem, together with a detailed analysis for the free boundary (the solid-liquid interface) particularly with respect to the asymptotic behavior as time t ↑ ∞ t \uparrow \infty where the steady state is attained.
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