Spatio-Temporal Dynamics of Reaction-Diffusion Patterns
Spatio-Temporal Dynamics of Reaction-Diffusion Patterns
复制标题
反应扩散模式的时空动力学
DOI：
10.1007/978-3-662-05281-5_2
复制
发表时间：
2003
影响因子：
2.4
通讯作者：
A. Scheel
中科院分区：
文献类型：
--
作者：
B. Fiedler;A. Scheel
在这次调查中，我们看看抛物型偏微分方程从动力系统的观点。动力系统理论的起源深深植根于天体力学，许多现代方面都可以追溯到庞加莱的巨大影响，动力系统理论主要关注点u 0的全局时间演化T（t）u 0 -以及这些点的集合-在或多或少抽象的相空间X中。在过去的世纪中，动力学概念如梯度流、不变流形、遍历性、移位动力学等的成功是巨大的--无论是从成就上还是从对新出现的问题和长期未决问题的活力上来衡量。
In this survey we look at parabolic partial differential equations from a dynamical systems point of view. With origins deeply rooted in celestial mechanics, and many modern aspects traceable to the monumental influence of Poincare, dynamical systems theory is mainly concerned with the global time evolution T(t)u 0 of points u 0 — and of sets of such points — in a more or less abstract phase space X. The success of dynamical concepts such as gradient flows, invariant manifolds, ergodicity, shift dynamics, etc. during the past century has been enormous — both as measured by achievement, and by vitality in terms of newly emerging questions and long-standing open problems.