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Existence of solutions to a phase‐field model for the isothermal solidification process of a binary alloy
Author(s) -
Rappaz J.,
Scheid J. F.
Publication year - 2000
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/(sici)1099-1476(200004)23:6<491::aid-mma120>3.0.co;2-4
Subject(s) - isothermal process , uniqueness , mathematics , lipschitz continuity , binary number , alloy , phase (matter) , field (mathematics) , binary alloy , thermodynamics , mathematical analysis , pure mathematics , materials science , metallurgy , physics , arithmetic , quantum mechanics
We investigate the well‐posedness of a phase‐field model for the isothermal solidification of a binary alloy due to Warren–Boettinger [12]. Existence of weak solution as well as regularity and uniqueness results are established under Lipschitz and boundedness assumptions for the non‐linearities. A maximum principle holds that guarantees the existence of a solution under physical assumptions on the non‐linearities. Copyright © 2000 John Wiley & Sons, Ltd.