On the steady-state continuous casting Stefan problem with nonlinear cooling

Chipot, Michel; Rodrigues, José-Francisco

doi:10.1090/qam/693880

Authors: Michel Chipot and José-Francisco Rodrigues
Journal: Quart. Appl. Math. 40 (1983), 476-491
MSC: Primary 35K05; Secondary 35R35, 80A20
DOI: https://doi.org/10.1090/qam/693880
MathSciNet review: 693880
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Abstract: 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.

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