A free boundary problem for interfaces in forward-backward lattice diffusion

Abstract

We examine the motion of phase interfaces in a diffusive lattice equation with bistable nonlinearity. We first show by heuristic arguments that the macroscopic evolution in the parabolic scaling limit is governed by a free boundary problem with hysteresis. Then, starting out from results for a piecewise affine nonlinearity whose backward region is a single point, we discuss ideas for a rigorous proof.