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Article Dans Une Revue Chinese Annals of Mathematics - Series B Année : 2017

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

Fabrice Bethuel
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Didier Smets
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Résumé

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.
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Dates et versions

hal-01480696 , version 1 (01-03-2017)

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  • HAL Id : hal-01480696 , version 1

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Fabrice Bethuel, Didier Smets. On the motion law of fronts for scalar reaction-diffusion equations with equal depth multiple-well potentials . Chinese Annals of Mathematics - Series B, 2017. ⟨hal-01480696⟩
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