STANDING WAVES OF REACTION-DIFFUSION EQUATIONS ON AN UNBOUNDED GRAPH WITH TWO VERTICES

被引：5

作者：

Iwasaki, Satoru ^{[1
]}

Jimbo, Shuichi ^{[2
]}

Morita, Yoshihisa ^{[3
]}

机构：

[1] Osaka Univ, Informat & Phys Sci, Grad Sch Informat Sci & Technol, Yamadaoka 1-5, Suita, Osaka 5650871, Japan

[2] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

[3] Ryukoku Univ, Dept Appl Math & Informat, Seta 5202194, Japan

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2022年 / 82卷 / 05期

关键词：

reaction-diffusion equation; unbounded metric graph; standing waves; stability; SCHNAKENBERG MODEL; EXISTENCE; STABILITY; STATES;

D O I：

10.1137/21M1454572

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We deal with bistable reaction-diffusion equations in a domain of a metric graph with two vertices, that is, a domain of multiple half-lines with two junctions connected by a line segment. We prove that there exist two types of standing waves: standing front waves and unimodal waves, if the line segment is long enough. We also numerically show the exact number of standing wave solutions for a cubic nonlinearity and for a piecewise linear case. The stability and instability of the standing wave solutions are also investigated. Standing waves play a role in blocking the front propagation.

引用

页码：1733 / 1763

页数：31

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