论文标题
Banach空间中渐近紧凑的共生的惯性歧管和叶子
Inertial manifolds and foliations for asymptotically compact cocycles in Banach spaces
论文作者
论文摘要
我们研究了Banach空间中抽象的共体给出的渐近紧凑的非自主动力学系统。我们的主要假设是由二次锥领域中的挤压特性（由不确定的二次lyapunov样函数给出的）和渐近紧凑性给出的。在这种情况下，可以像正常双曲歧管理论一样重建叶面。我们的方法允许统一许多局部和非局部不变流形的“实用”理论，例如稳定/不稳定/中心的歧管和惯性歧管，此外，它通常会导致其存在的最佳条件。 我们提供了半连接抛物线方程和中性延迟方程的应用，其中频率定理用于构建恒定的锥体场。
We study asymptotically compact nonautonomous dynamical systems given by abstract cocycles in Banach spaces. Our main assumptions are given by a squeezing property in a quadratic cone field (given by a family of indefinite quadratic Lyapunov-like functionals) and asymptotic compactness. Under such conditions it is possible to reconstruct foliations as in the theory of normally hyperbolic manifolds. Our approach allows to unify many "practical" theories of local and nonlocal invariant manifolds, such as stable/unstable/center manifolds and inertial manifolds, and, moreover, it often leads to optimal conditions for their existence. We give applications for semilinear parabolic equations and neutral delay equations, where the Frequency Theorem is used to construct constant cone fields.
