Fisher-KPP equation with Robin boundary conditions on the real half line

被引：0

作者：

Suo, Jinzhe ^{[1
]}

Tan, Kaiyuan ^{[1
,2
]}

机构：

[1] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China

[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2022年 / 222卷

基金：

中国国家自然科学基金;

关键词：

Fisher-KPP equation; Robin boundary condition; Entire solution; Traveling wave solution; Asymptotic behavior; TRAVELING-WAVE SOLUTIONS; REACTION-DIFFUSION EQUATIONS; DIFFERENTIAL-EQUATIONS;

D O I：

10.1016/j.na.2022.112933

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Fisher-KPP equation with Robin boundary conditions on the half line. We show that this problem has even number of nonnegative stationary solutions, which are ordered, a stable one is sandwiched by two unstable ones. Then we construct several types of entire solutions between them, each entire solution connects an unstable stationary solution with a stable one. In particular, we construct two types of entire solutions U-c(x, t) and U(x, t) connecting 0 and the smallest positive stationary solution. In addition, U-c tend to the traveling wave solution with speed c as t -> -infinity in a moving frame, and U(x, t) enjoys convexity. This paper extends the recent results of Lou, Lu and Morita in Lou et al. (2020) from Dirichlet boundary condition to Robin boundary condition. (c) 2022 Elsevier Ltd. All rights reserved.

引用

页数：14

共 50 条

[41] Doubly nonlocal Fisher-KPP equation: Speeds and uniqueness of traveling waves [J].

Finkelshtein, Dmitri ;

Kondratiev, Yuri ;

Tkachov, Pasha .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 475 (01) :94-122

[42] Forced waves of saturation type for Fisher-KPP equation in a shifting environment [J].

Guo, Jong-Shenq ;

Poh, Amy Ai Ling ;

Wu, Chin-Chin .

APPLIED MATHEMATICS LETTERS, 2023, 140

[43] The Bramson delay in a Fisher-KPP equation with log-singular nonlinearity [J].

Bouin, Emeric ;

Henderson, Christopher .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2021, 213

[44] New travelling wave solutions for the Fisher-KPP equation with general exponents [J].

Sánchez-Valdés, A ;

Hernández-Bermejo, B .

APPLIED MATHEMATICS LETTERS, 2005, 18 (11) :1281-1285

[45] Uniqueness and stability of forced waves for the Fisher-KPP equation in a shifting environment ☆ [J].

Guo, Jong-Shenq ;

Guo, Karen ;

Shimojo, Masahiko .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2024, 247

[46] Hopf bifurcation of traveling wave solutions of delayed Fisher-KPP equation [J].

Yang, Gaoxiang .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 220 :213-220

[47] The spreading speed of solutions of the non-local Fisher-KPP equation [J].

Penington, Sarah .

JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 275 (12) :3259-3302

[48] Propagation dynamics of Fisher-KPP equation with time delay and free boundaries [J].

Sun, Ningkui ;

Fang, Jian .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2019, 58 (04)

[49] Tropical discretization: ultradiscrete Fisher-KPP equation and ultradiscrete Allen-Cahn equation [J].

Murata, Mikio .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2013, 19 (06) :1008-1021

[50] Propagation dynamics of a nonlocal dispersal Fisher-KPP equation in a time-periodic shifting habitat [J].

Zhang, Guo-Bao ;

Zhao, Xiao-Qiang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (06) :2852-2885

← 1 2 3 4 5 →