On the slowness of phase boundary motion in one space dimension
Lia Bronsard, Robert V. Kohn · Communications on Pure and Applied Mathematics · 1990
Abstract We study the limiting behavior of the solution of with a Neumann boundary condition or an appropriate Dirichlet condition. The analysis is based on “energy methods”. We assume that the initial data has a “transition layer structure”, i.e.,uϵ≈ ±+M 1 except near finitely many transition points. We show that, in the limit as ϵ → 0, the solution maintains its transition layer structure, and the transition points move slower than any power of ϵ.