TIKHONOV'S THEOREM AND QUASI-STEADY STATE
TIKHONOV'S THEOREM AND QUASI-STEADY STATE
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DOI：
10.3934/dcdsb.2011.16.945
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发表时间：
2011-10-01
影响因子：
1.2
通讯作者：
Walcher, Sebastian
中科院分区：
文献类型：
--
作者：
Noethen, Lena;Walcher, Sebastian
有一个系统的方法，通过经典理论的Tikhonov和Fenichel准稳态现象的渐近性质。这一观察允许，一方面，解决收敛问题，这是远离平凡的渐近展开。另一方面，即使人们认为收敛是理所当然的，这种方法也会产生一种自然的方法来计算慢流形上的简化系统，其简化方程通常比通过特设方法获得的方程更简单。特别地，简化系统总是有理的。本文包括讨论的必要条件和充分条件适用的吉洪诺夫和Fenichel的定理，计算问题和直接确定的减少系统。结果被应用到几个相关的例子。
There exists a systematic approach to asymptotic properties for quasi-steady state phenomena via the classical theory of Tikhonov and Fenichel. This observation allows, on the one hand, to settle convergence issues, which are far from trivial in asymptotic expansions. On the other hand, even if one takes convergence for granted, the approach yields a natural way to compute a reduced system on the slow manifold, with a reduced equation that is frequently simpler than the one obtained by the ad hoc approach. In particular, the reduced system is always rational. The paper includes a discussion of necessary and sufficient conditions for applicability of Tikhonov's and Fenichel's theorems, computational issues and a direct determination of the reduced system. The results are applied to several relevant examples.