Convergence of the Cahn–Hilliard Equation to the Mullins–Sekerka Problem in Spherical Symmetry

We show that, as →0, the solution of the Cahn–Hilliard equation[formula]converges to a solution of the Mullins–Sekerka problem[formula]whereνdenotes a normal,Vthe normal velocity andKthe sum of principal curvatures of the interface, provided the solutions are radially symmetric. We use energy type estimates to show that the solution of the Cahn–Hilliard equation can be approximated by the well–known stationary wave solution that corresponds to the potentialW.