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

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 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.