非均匀指数二分法的新概念及其在回拉和前向吸引子理论中的应用

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-09-04 DOI:10.1088/1361-6544/ad700a

José A Langa, Rafael Obaya, Alexandre N Oliveira-Sousa

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引用次数: 0

摘要

在这项研究中，我们研究了与非自治微分方程相关的演化过程的非均匀指数二分法以及回拉和前向吸引子的存在性。我们定义了非均匀指数二分法的新概念，并提供了几个例子，研究了它与标准概念的关系，并建立了扰动下的稳健性。我们提供了与指数二分法相关的可接纳性对的动力学解释，以获得回拉和前向吸引子的存在性。我们将这些抽象结果应用于常微分方程和抛物线微分方程。

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New notion of nonuniform exponential dichotomy with applications to the theory of pullback and forward attractors

In this work we study nonuniform exponential dichotomies and existence of pullback and forward attractors for evolution processes associated to nonautonomous differential equations. We define a new concept of nonuniform exponential dichotomy, for which we provide several examples, study the relation with the standard notion, and establish a robustness under perturbations. We provide a dynamical interpretation of admissibility pairs related with exponential dichotomies to obtain existence of pullback and forward attractors. We apply these abstract results for ordinary and parabolic differential equations.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.