Slow motion for gradient systems with equal depth multiple-well potentials

For scalar reaction–diffusion in one space dimension, it has been known for a long time that fronts move with an exponentially small speed for potentials with several distinct minimizers. The purpose of this paper is to provide a similar result in the case of systems. Our method relies on a careful study of the evolution of localized energy. This approach also has the advantage of relaxing the preparedness assumptions on the initial datum.