Unbounded Asymmetric Stationary Solutions of Lattice Nagumo Equations

被引：1

作者：

Hesoun, Jakub ^{[1
,2
]}

Stehlik, Petr ^{[1
,2
]}

Volek, Jonas ^{[1
,2
]}

机构：

[1] Univ West Bohemia, Fac Appl Sci, Dept Math, Univ 8, Plzen 30100, Czech Republic

[2] Univ West Bohemia, Fac Appl Sci, NTIS, Univ 8, Plzen 30100, Czech Republic

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2024年 / 23卷 / 02期

关键词：

Nagumo equation; Lattice differential equation; Patterns; Unbounded solutions; Equivalence class; TRAVELING-WAVES; EXISTENCE;

D O I：

10.1007/s12346-023-00904-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：14

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