Global solutions to a degenerate solutal phase-field model for the solidification of a binary alloy |
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| Affiliation: | 1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 101 Vernadsky Avenue, bldg 1, 119526 Moscow, Russia;2. Bauman Moscow State Technical University, 5 Second Baumanskaya Street, 105005 Moscow, Russia |
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| Abstract: | We consider a degenerate solutal phase-field model for the solidification of a binary alloy. This model is devoted to the evolution of the phase-field variable together with the relative concentration of the alloy for which the equation may degenerate. The existence of global weak solutions is proved for the degenerate case with a loss of regularity for the concentration in comparison with the non-degenerate case. |
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