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

For scalar reaction-diffusion in one space dimension, it is known for a long time that fronts move with an exponentially small speed for potentials with several distinct mini- mizers. The purpose of this paper is to provide a similar result in the case of systems. Our method relies on a careful stud...

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Bibliographic Details
Published in:arXiv.org 2009-10
Main Authors: Bethuel, Fabrice, Smets, Didier, Orlandi, Giandomenico
Format: Article
Language:English
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Datum (elevation)
Online Access:Get full text
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Summary:For scalar reaction-diffusion in one space dimension, it is known for a long time that fronts move with an exponentially small speed for potentials with several distinct mini- mizers. 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 has the advantage to relax the preparedness assumptions on the initial datum.
ISSN:2331-8422