跟踪奇异扰动 ODE 系统中与快速时间相关的非自主吸引子

IF 2.4 2区 数学 Q1 MATHEMATICS
Iacopo P. Longo , Rafael Obaya , Ana M. Sanz
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引用次数: 0

摘要

从追踪非自主吸引子的角度,给出了关于依赖于快速时间的慢速 ODE 系统中快速运动行为的新结果。在相当普遍的假设条件下,包括层问题解的均匀终极有界性,考虑了膨胀回拉吸引子。一般来说,我们不能不考虑膨胀版的回拉吸引子,但在吸引子的纤维投影图的连续性条件下是可能的。慢-快系统在慢时间的每个固定正值上的解的极限问题也得到了处理,在这种表述中,临界集是由回拉吸引子的纤维联合给出的。这些结果可以看作是经典提霍诺夫定理在非自治环境下的扩展。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tracking nonautonomous attractors in singularly perturbed systems of ODEs with dependence on the fast time

New results on the behaviour of the fast motion in slow-fast systems of ODEs with dependence on the fast time are given in terms of tracking of nonautonomous attractors. Under quite general assumptions, including the uniform ultimate boundedness of the solutions of the layer problems, inflated pullback attractors are considered. In general, one cannot disregard the inflated version of the pullback attractor, but it is possible under the continuity of the fiber projection map of the attractor. The problem of the limit of the solutions of the slow-fast system at each fixed positive value of the slow time is also treated and in this formulation the critical set is given by the union of the fibers of the pullback attractors. The results can be seen as extensions of the classical Tikhonov theorem to the nonautonomous setting.

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来源期刊
CiteScore
4.40
自引率
8.30%
发文量
543
审稿时长
9 months
期刊介绍: The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics
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