反应扩散方程的混沌初值和边界值问题

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-10-15 DOI:10.1016/j.jmaa.2024.128946

Pengxian Zhu, Qigui Yang

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引用次数: 0

摘要

本文研究了反应扩散方程的初值和边界值问题，该方程可视为平动 Fisher-KPP 方程的线性化形式。结果表明，当反应扩散方程的三个参数在一个特定表面上方变化时，初值和边界值问题是混乱的。然而，在一个特定的初值子集内，在该曲面上和曲面下都能得到稳定的解。我们还进一步研究了非均质初始边界值问题的混沌性和稳定性。最后，还提供了一些数值示例来说明所获结果的有效性。

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Chaos of the initial and boundary value problems for the reaction-diffusion equations

This paper investigates an initial and boundary value problem for the reaction-diffusion equations, which can be considered as a linearized form of the advective Fisher-KPP equations. It is demonstrated that the initial and boundary value problem is chaotic when the three parameters of the reaction-diffusion equation vary above a specific surface. However, stable solutions are obtained both on and below this surface within a particular subset of initial values. The chaos and stability of the nonhomogeneous initial boundary value problem are further studied. Finally, some numerical examples are provided to illustrate the validity of the obtained results.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.