Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 267-282 |
Number of pages | 16 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 140 |
Issue number | 3 |
DOIs | |
Publication status | Published - 15 Jun 2000 |