不具有紧致性的偏泛函微分方程的约简原理

IF 0.8 4区数学 Q2 MATHEMATICS

Electronic Journal of Differential Equations Pub Date : 2023-06-20 DOI:10.58997/ejde.2023.39

Meryem El Attaouy, K. Ezzinbi, Gaston Mandata ˜N'Guerekata

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引用次数: 0

摘要

本文建立了不具有线性部分生成的半群紧性的偏泛函微分方程的一个约简原理。在比线性部分生成的C0半群的紧性更一般的条件下，我们建立了与偏泛函微分方程的线性部分相关的C0半群的拟紧性。该结果允许构造由在有限维空间中提出的常微分方程提出的简化系统。通过这个结果，我们研究了偏泛函微分方程的概自同构和概周期解的存在性。为了举例说明，我们研究了一个运输模型。

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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Reduction principle for partial functional differential equation without compactness

This article establishes a reduction principle for partial functional differential equation without compactness of the semigroup generated by the linear part. Under conditions more general than the compactness of the C0-semigroup generated by the linear part, we establish the quasi-compactness of the C0-semigroup associated to the linear part of the partial functional differential equation. This result allows as to construct a reduced system that is posed by an ordinary differential equation posed in a finite dimensional space. Through this result we study the existence of almost automorphic and almost periodic solutions for partial functional differential equations. For illustration, we study a transport model.

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来源期刊

Electronic Journal of Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

3 months

期刊介绍： All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.