For scalar reaction-diffusion equations in one space dimension, it is 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 the localized energy. This approach has the advantage to relax the preparedness assumptions on the initial datum.[PS]
Slow motion for gradient systems with equal depth multiple-well potentials
ORLANDI, Giandomenico;
2011-01-01
Abstract
For scalar reaction-diffusion equations in one space dimension, it is 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 the localized energy. This approach has the advantage to relax the preparedness assumptions on the initial datum.[PS]
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