On the motion law of fronts for scalar reaction-diffusion equations with equal depth multiple-well potentials

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• 作者：Fabrice Bethuel ; Didier Smets
• 关键词：Reaction ; diffusion systems ; Parabolic equations ; Singular limits
• 刊名：Chinese Annals of Mathematics, Series B
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：38
• 期：1
• 页码：83-148
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1860-6261
• 卷排序：38

文摘

Slow motion for scalar Allen-Cahn type equation is a well-known phenomenon, precise motion law for the dynamics of fronts having been established first using the socalled geometric approach inspired from central manifold theory (see the results of Carr and Pego in 1989). In this paper, the authors present an alternate approach to recover the motion law, and extend it to the case of multiple wells. This method is based on the localized energy identity, and is therefore, at least conceptually, simpler to implement. It also allows to handle collisions and rough initial data.