The Dynamics of a Conserved Phase Field System: Stefan-like, Hele-Shaw, and Cahn-Hilliard Models as Asymptotic Limits

The dynamics of a conserved phase field system for a free boundary, that is, u t +1/2lφ t =KΔu, −τφ t =ξ 2 Δ[ξ 2 Δφ+f(φ)/a+2u], are studied asymptotically. Many of the major macroscopic free-boundary problems arise as limits in various scalings