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An analysis of a phase-field model for isothermal binary alloy solidification with convection under the influence of magnetic field. (English) Zbl 1387.80004
Summary: This paper is devoted to the study of a new phase-field model with convection under the influence of magnetic field for the isothermal solidification of binary mixtures in two-dimensional geometry. A brief description of the system governing the model is given. The existence of weak solutions as well as the regularity and uniqueness results are established under certain conditions on the nonlinearities. A maximum principle under additional assumptions are also derived. A numerical calculation is performed.

MSC:
80A22 Stefan problems, phase changes, etc.
35B50 Maximum principles in context of PDEs
35Q35 PDEs in connection with fluid mechanics
Software:
DASSL; VLUGR2
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References:
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