A phase-field model for the isothermal solidification process of a binary alloy - Kessler, Daniel; Kruger, Olivier; Rappaz, Jacques; Scheid, Jean-Frangois (Computer Assisted Methods in Engineering and Science, 2023)
We study a phase-field model for the isothermal solidification of a binary alloy which involves the relative concentration and the order parameter. We prove the existence of weak solutions as well as regularity and uniqueness results under Lipschitz and boundeness assumptions for the nonlinearities. A maximum principle holds that justifies these assumptions. A numerical approximation and some numerical results are also presented.