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 manifo...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.展开更多
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.
