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Local existence of solutions of a three phase‐field model for solidification
Author(s) -
Caretta Bianca Morelli Calsavara,
Boldrini José Luiz
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1094
Subject(s) - uniqueness , mathematics , field (mathematics) , partial differential equation , phase (matter) , parabolic partial differential equation , phase field models , crystallization , mathematical analysis , thermodynamics , pure mathematics , physics , quantum mechanics
In this article we discuss the local existence and uniqueness of solutions of a system of parabolic differential partial equations modeling the process of solidification/melting of a certain kind of alloy. This model governs the evolution of the temperature field, as well as the evolution of three phase‐field functions; the first two describe two different possible solid crystallization states and the last one describes the liquid state. Copyright © 2008 John Wiley & Sons, Ltd.