Calculus of Variations and Geometric Measure Theory
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F. Bethuel - G. Orlandi - D. Smets

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

created by orlandi on 27 Dec 2009
modified on 09 Jan 2011


Published Paper

Inserted: 27 dec 2009
Last Updated: 9 jan 2011

Journal: J. Differential Equations
Volume: 250
Number: 1
Pages: 53-94
Year: 2011


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.

Keywords: reaction-diffusion systems, interfaces, fronts, slow motion


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