Existence of solutions to a phase-field model for the isothermal solidification process of a binary alloy

Authors
Rappaz, J Scheid, JF
Citation
J. Rappaz et Jf. Scheid, Existence of solutions to a phase-field model for the isothermal solidification process of a binary alloy, MATH METH A, 23(6), 2000, pp. 491-513
Citations number
12
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN journal
01704214 → ACNP
Volume
23
Issue
6
Year of publication
2000
Pages
491 - 513
Database
ISI
SICI code
0170-4214(200004)23:6<491:EOSTAP>2.0.ZU;2-K
Abstract
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 establish ed under Lipschitz and boundedness assumptions for the non-linearities. A m aximum principle holds that guarantees the existence of a solution under ph ysical assumptions on the non-linearities. Copyright (C) 2000 John Wiley & Sons, Ltd.