一类报警-出租车系统的全局可解性与稳定性

IF 1.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2023-05-27 DOI:10.1137/22M1477143

Hai-yang Jin, Zhian Wang, Leyun Wu

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引用次数: 2

摘要

本文研究一类报警-出租车系统经典解的全局有界性和稳定性，该系统描述了在物种受到捕食者威胁时，防盗报警假设是一种重要的反捕食行为机制。与已有的捕食趋向性系统相比，报警趋向性系统耦合结构更为复杂，并且需要对主要捕食者密度进行梯度估计以获得解的全局有界性。通过基于Neumann半群平滑性质的复杂耦合能量估计，建立了具有Neumann边界条件的二维系统全局有界解的存在性，进一步证明了系统参数在一定条件下共存齐次稳态的全局稳定性。

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Global Solvability and Stability of an Alarm-Taxis System

This paper is concerned with the global boundedness and stability of classical solutions to an alarm-taxis system describing the burglar alarm hypothesis as an important mechanism of anti-predation behavior when species are threaten by predators. Compared to the existing prey-taxis systems, the alarm-taxis system has more complicated coupling structure and additionally requires the gradient estimate of the primary predator density to attain the global boundedness of solutions. By the sophisticated coupling energy estimates based on the Neumann semigroup smoothing properties, we establish the existence of globally bounded solutions in two dimensions with Neumann boundary conditions and furthermore prove the global stability of co-existence homogeneous steady states under certain conditions on the system parameters.

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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.