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arXiv 0909.5315math.APmath.DS
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等深多势阱梯度系统的慢运动

Slow motion for gradient systems with equal depth multiple-well potentials

Fabrice Bethuel, Didier Smets, Giandomenico Orlandi

摘要:

对于一维空间中的标量反应扩散,人们长期以来都知道,对于具有几个不同的极小子的势,前沿以指数小的速度移动。本文的目的是在系统的情况下提供一个类似的结果。我们的方法依赖于对局部能量演化的仔细研究。这种方法的优点是放松了对初始数据的准备假设。

英文摘要:

For scalar reaction-diffusion in one space dimension, it is known for a long time that fronts move with an exponentially small speed for potentials with several distinct mini- mizers. The purpose of this paper is to provide a similar result in the case of systems. Our method relies on a careful study of the evolution of localized energy. This approach has the advantage to relax the preparedness assumptions on the initial datum.

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