Analysis of a two-phase field model for the solidification of an alloy |
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Authors: | José Luiz Boldrini |
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Institution: | a IMECC, University of Campinas, CP 6065, 13083-970, Campinas-SP, Brazil b Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain |
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Abstract: | In this paper we present some theoretical results for a system of nonlinear partial differential equations that provide a phase field model for the solidification/melting of a metallic alloy. It is assumed that two different kinds of crystallization are possible. Consequently, the unknowns are the temperature τ and the phase field functions u and v. The time derivatives ut and vt appear in the equation for τ (the heat equation). On the other hand, the equations for u and v contain nonlinear terms where we find τ. |
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Keywords: | Solidification models Phase field models Parabolic partial differential equations Existence Uniqueness Regularity |
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