Chaos of Multi-dimensional Weakly Hyperbolic Equations with General Nonlinear Boundary Conditions

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED Journal of Nonlinear Science Pub Date : 2024-05-02 DOI:10.1007/s00332-024-10038-2

Qiaomin Xiang, Qigui Yang

引用次数: 0

Abstract

This paper is dedicated to investigating the chaos of a initial-boundary value (IBV) problem of a multi-dimensional weakly hyperbolic equation subject to two general nonlinear boundary conditions (NBCs). The existence and uniqueness of solution for the IBV problem are established. By employing the snap-back repeller and heteroclinic cycle theories, it has been proven that the IBV problem with a linear and a general NBCs exhibits chaos in the sense of both Devaney and Li–Yorke. Furthermore, these chaotic results are extended to the IBV problem with two general NBCs. Two stability criteria of the IBV problem are established, respectively, for the corresponding two cases of boundary conditions. Finally, numerical simulations are presented to illustrate the theoretical results.

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具有一般非线性边界条件的多维弱双曲方程的混沌问题

本文致力于研究受两个一般非线性边界条件（NBC）影响的多维弱双曲方程的初界值（IBV）问题的混沌性。建立了 IBV 问题解的存在性和唯一性。通过运用快退排斥器和异质周期理论，证明了具有线性和一般 NBCs 的 IBV 问题表现出 Devaney 和 Li-Yorke 意义上的混沌。此外，这些混沌结果还扩展到了具有两个一般 NBC 的 IBV 问题。针对相应的两种边界条件情况，分别建立了 IBV 问题的两个稳定性准则。最后，通过数值模拟来说明理论结果。

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

Journal of Nonlinear Science 数学-力学

CiteScore

5.00

自引率

3.30%

发文量

审稿时长

4.5 months

期刊介绍： The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.