Local existence of solutions of a three phase-field model for solidification

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 p...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2009-08, Vol.32 (12), p.1496-1518
Main Authors: Caretta, Bianca Morelli Calsavara, Boldrini, José Luiz
Format: Article
Language:English
Subjects:
alloy
Exact sciences and technology
existence of solution
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
parabolic equation
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
phase field
Sciences and techniques of general use
solidification
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.1094