论文标题
无限维度方程的慢歧管
Slow Manifolds for Infinite-Dimensional Evolution Equations
论文作者
论文摘要
我们将经典的有限维芬切尔理论扩展到两个方向上，以无限维度。在相当弱的假设下，我们表明，通过相应的慢速流很好地近似地近似于无限尺寸快速缓慢系统的解。之后，我们在慢速方程的线性部分上更加限制的假设下，构建了一个慢歧管$ s_ {ε，ζ} $的两参数家族。第二个参数$ζ$不出现在有限维设置中，并描述了快速衰减部分中慢速可变空间及其补体的一定分裂。有限维设置包含是$ s_ {ε，ζ} $不取决于$ζ$的特殊情况。最后，我们将新技术应用于偏微分方程的快速缓慢系统的三个示例。
We extend classical finite-dimensional Fenichel theory in two directions to infinite dimensions. Under comparably weak assumptions we show that the solution of an infinite-dimensional fast-slow system is approximated well by the corresponding slow flow. After that we construct a two-parameter family of slow manifolds $S_{ε,ζ}$ under more restrictive assumptions on the linear part of the slow equation. The second parameter $ζ$ does not appear in the finite-dimensional setting and describes a certain splitting of the slow variable space in a fast decaying part and its complement. The finite-dimensional setting is contained as a special case in which $S_{ε,ζ}$ does not depend on $ζ$. Finally, we apply our new techniques to three examples of fast-slow systems of partial differential equations.
