The Quasistationary Phase Field Equations with Neumann Boundary Conditions

We prove that the quasistationary phase field equations∂t(u+ )−Δu=f, where W(t)=(t2−1)2 is a double-well potential, admit a solution, when the space dimension n 3, and that the solutions converge for →0 to solutions of the Stefan problem with Gibbs–Thomson law.