Principal Spectral Theory of Time-Periodic Nonlocal Dispersal Cooperative Systems and Applications

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-04 DOI:10.1137/22m1543902

Yan-Xia Feng, Wan-Tong Li, Shigui Ruan, Ming-Zhen Xin

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Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 4040-4083, June 2024.
Abstract. This paper is concerned with the principal spectral theory of time-periodic cooperative systems with nonlocal dispersal and Neumann boundary condition. First we present a sufficient condition for the existence of principal eigenvalues by using the theory of resolvent positive operators with their perturbations. Then we establish the monotonicity of principal eigenvalues with respect to the frequency and investigate the limiting properties of principal eigenvalues as the frequency tends to zero or infinity. We also study the effects of dispersal rates and dispersal ranges on the principal eigenvalues, and the difficulty is that principal eigenvalues of time-periodic cooperative systems with Neumann boundary conditions are not monotone with respect to the domain. Finally, we apply our theory to a man-environment-man epidemic model and consider the impacts of dispersal rates, frequency, and dispersal ranges on the basic reproduction number and positive time-periodic solutions.

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时间周期性非局部分散合作系统的主频谱理论及其应用

SIAM 数学分析期刊》，第 56 卷第 3 期，第 4040-4083 页，2024 年 6 月。摘要本文主要研究具有非局部分散和 Neumann 边界条件的时周期协同系统的主谱理论。首先，我们利用带扰动的解析正算子理论提出了主特征值存在的充分条件。然后，我们建立了主特征值相对于频率的单调性，并研究了当频率趋于零或无穷大时主特征值的极限特性。我们还研究了分散率和分散范围对主特征值的影响，难点在于具有诺伊曼边界条件的时间周期合作系统的主特征值与域无关的单调性。最后，我们将理论应用于人-环境-人流行病模型，并考虑了分散率、频率和分散范围对基本繁殖数和正时间周期解的影响。

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

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.