Evaporation of droplets in the two-dimensional Ginzburg-Landau equation

We consider the problem of coarsening in two dimensions for the real (scalar) Ginzburg-Landau equation. This equation has exactly two stable stationary solutions, the constant functions +1 and -1. We assume most of the initial condition is in the `-1' phase with islands of `+1' phase. We use invariant manifold techniques to prove that the boundary of a circular island moves according to Allen-Cahn curvature motion law. We give a criterion for non-interaction of two arbitrary interfaces and a criterion for merging of two nearby interfaces.