连接一个直接和Galerkin方法在无限维慢流形
Connecting a direct and a Galerkin approach to slow manifolds in infinite dimensions
摘要：
本文研究了无限维发展方程的慢流形。我们比较两种方法：一个抽象的发展方程框架和有限维谱伽辽金近似。我们证明了在适当的条件下，每种方法内构造的慢流形是渐近接近的。证明是基于Lyapunov-Perron方法和巴拿赫空间尺度上慢流形的局部图的比较。总之，我们的主要结果使我们能够根据特定的快慢系统所带来的技术挑战，在慢不变流形的不同特征之间进行改变。
英文摘要：
In this paper, we study slow manifolds for infinite-dimensional evolution equations. We compare two approaches: an abstract evolution equation framework and a finite-dimensional spectral Galerkin approximation. We prove that the slow manifolds constructed within each approach are asymptotically close under suitable conditions. The proof is based upon Lyapunov-Perron methods and a comparison of the local graphs for the slow manifolds in scales of Banach spaces. In summary, our main result allows us to change between different characterizations of slow invariant manifolds, depending upon the technical challenges posed by particular fast-slow systems.
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