Attractive sets of periodic integrodifference equations under discretization

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-04 DOI:10.1080/10236198.2023.2262613

Peter E. Kloeden, Christian Pötzsche

引用次数: 0

Abstract

We consider periodic difference equations in infinite-dimensional Banach spaces possessing compact asymptotically stable set A. It is established that such A persists under spatial discretizations by means of projection methods as nearby closed and bounded uniformly asymptotically stable sets, which moreover converge to A in the Hausdorff metric for increasingly more accurate schemes. The proof is based on a Lyapunov function guaranteed by an ambient converse theorem and a pullback construction. As application serves integrodifference equations on spaces of continuous and p-integrable functions over a compact habitat.

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离散化下周期积分差分方程的吸引集

考虑无限维Banach空间中具有紧的渐近稳定集A的周期差分方程，利用投影方法证明了在空间离散化下，A是邻近的闭有界一致渐近稳定集，并且在越来越精确的格式下收敛于Hausdorff度量中的A。该证明基于由环境逆定理和回拉构造保证的李雅普诺夫函数。作为在紧生境上连续函数和p可积函数空间上的积分差分方程的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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