The quasistationary phase field equations with Neumann boundary conditions

We prove that the quasistationary phase field equations partial derivative(t)(u + phi) - Delta u = f, - 2 epsilon Delta phi + 1/epsilon W'(phi) = u, where W(t) = (t(2) - 1)(2) is a double-well potential, admit a solution, wh en the space dimension n less than or equal to 3, and that the solutions co nverge for epsilon --> 0 to solutions of the Stefan problem with Gibbs-Thom son law. (C) 2000 Academic Press.