On the Motion Law of Fronts for Scalar Reaction-Diffusion Equations with Equal Depth Multiple-Well Potentials

(整期优先)网络出版时间:2017-01-11
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SlowmotionforscalarAllen-Cahntypeequationisawell-knownphenomenon,precisemotionlawforthedynamicsoffrontshavingbeenestablishedfirstusingthesocalledgeometricapproachinspiredfromcentralmanifoldtheory(seetheresultsofCarrandPegoin1989).Inthispaper,theauthorspresentanalternateapproachtorecoverthemotionlaw,andextendittothecaseofmultiplewells.Thismethodisbasedonthelocalizedenergyidentity,andistherefore,atleastconceptually,simplertoimplement.Italsoallowstohandlecollisionsandroughinitialdata.