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| On the Motion Law of Fronts for Scalar Reaction-Diffusion Equations with Equal Depth Multiple-Well Potentials |
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Citation： |
Fabrice BETHUEL,Didier SMETS.On the Motion Law of Fronts for Scalar Reaction-Diffusion Equations with Equal Depth Multiple-Well Potentials[J].Chinese Annals of Mathematics B,2017,38(1):83~148 |
| Page view： 695
Net amount： 668 |
Authors： |
Fabrice BETHUEL; Didier SMETS |
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| Abstract： |
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 so-called 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. |
Keywords： |
Reaction-diffusion systems, Parabolic equations, Singular limits |
Classification： |
35K40, 35K57, 35K61 |
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