晶格南云方程的无界非对称静态解

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2023-12-18 DOI:10.1007/s12346-023-00904-x

Jakub Hesoun, Petr Stehlík, Jonáš Volek

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引用次数: 0

摘要

在这篇论文中，我们提供了网格纳古莫方程的一类无约束非对称静止解的完整特征。我们证明，对于任何双稳态立方非线性和任意扩散率，都存在发散到无穷大的一般非对称静止解的两参数等价类集合。我们的主要工具是迭代镜像技术，该技术可适用于与晶格方程相关的其他问题。最后，我们将这一结果归纳为一大类反应函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Unbounded Asymmetric Stationary Solutions of Lattice Nagumo Equations

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Unbounded Asymmetric Stationary Solutions of Lattice Nagumo Equations

In this paper we provide a complete characterization of a class of unbounded asymmetric stationary solutions of the lattice Nagumo equations. We show that for any bistable cubic nonlinearity and arbitrary diffusion rate there exists a two-parametric set of equivalence classes of generally asymmetric stationary solutions which diverge to infinity. Our main tool is an iterative mirroring technique which could be applicable to other problems related to lattice equations. Finally, we generalize the result for a broad class of reaction functions.

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.